Systems and methods for learning across multiple chemical sensing units using a mutual latent representation

ABSTRACT

Systems and methods for training models across multiple sensing units in a chemical sensing system are described. The chemical sensing system comprises at least one computer processor and at least one computer readable medium including instructions that, when executed by the at least one computer processor, cause the chemical sensing system to perform a training process. The training process comprises accessing a training dataset including first values representing first signals output from a first chemical sensing unit of multiple chemical sensing units, and second values representing second signals output from a second chemical sensing unit of the multiple chemical sensing units, and training a set of models to relate the first values and the second values to a mutual latent representation using the training dataset.

RELATED APPLICATIONS

This application claims priority under 35 U.S.C. § 119(e) to U.S.Provisional Application 62/809,364 entitled, “CHEMICAL SENSING SYSTEMSFOR MANY CHEMICAL SENSING SENSORS CONSIDERING WEAK SUPERVISION ANDSEQUENTIAL INFORMATION,” filed Feb. 22, 2019, the entire contents ofwhich is incorporated by reference herein.

BACKGROUND

Direct and indirect interactions with chemicals in the environment canadversely affect human physical and mental health. Chemicals in theenvironment may include, for example, particulates and volatile organiccompounds (“VOCs”) generated at hospitals, chemicals emanating from foodspoilage, VOCs exhaled in breath, industrial and automobile exhausts,and early indications of processes such as disease, food spoilage, andcombustion.

SUMMARY

Aspects of the present application relate to a real-time, low-cost,low-power, miniature chemical sensing system capable of simultaneouslysensing multiple chemicals. The system includes a component, which maybe a sensor chip, that contains an array of nanocomposite sensors. Thesesensors are configured to produce a unique fingerprint for any givenchemical or combination of chemicals. Each nanocomposite is, in general,sensitive to a particular chemical (e.g., ammonia), but is alsocross-sensitive to other chemicals (e.g., acetone, carbon dioxide).Although individual sensors may lack high selectivity, an array ofsensors formed from the combination of cross-sensitive polymers cangenerate a response pattern specific to a particular chemicalcombination. This approach allows for targeting a broad range ofchemical analytes for identification and quantification. Additionally,this approach allows for creating large, centralized reference databasesof chemical fingerprints, which can then be used to trainmachine-learning models capable of deconvolving the fingerprint of acomplex mixture of chemicals.

According to some embodiments, a chemical sensing system is providedcomprising at least one computer processor and at least one computerreadable medium including instructions that, when executed by the atleast one computer processor, cause the chemical sensing system toperform a training process. The training process may comprise: accessinga training dataset including first values representing first signalsoutput from a first chemical sensing unit of multiple chemical sensingunits, and second values representing second signals output from asecond chemical sensing unit of the multiple chemical sensing units; andtraining a set of models to relate the first values and the secondvalues to a mutual latent representation using the training dataset.

In some embodiments, training the set of models may include training oneor more first models of the set of models to relate the first valuesrepresenting the first signals to a first feature representation, and torelate the second values representing the second signals to a secondfeature representation.

In some embodiments, training the set of models may include training oneor more second models of the set of models to relate the first featurerepresentation to a first latent representation, and to relate thesecond feature representation to a second latent representation.

In some embodiments, training the set of models may include training oneor more third models of the set of models to relate the first latentrepresentation to the mutual latent representation, and to relate thesecond latent representation to the mutual latent representation.

In some embodiments, training the set of models may include training afourth model of the set of models to generate inferences based on themutual latent representation.

In some embodiments, training the one or more first models to relate thefirst values representing the first signals to the first featurerepresentation may comprise training a first model of the one or morefirst models to determine a first mapping between the first valuesrepresenting the first signals and the first feature representation, andtraining the one or more second models to relate the second valuesrepresenting the second signals to the second feature representationcomprises training a second model of the one or more first models todetermine a second mapping between the second values representing thesecond signals and the second feature representation.

In some embodiments, the first model of the one or more first models andthe second model of the one or more first models may be a same model andthe first mapping and the second mapping may be a same mapping.

In some embodiments, training the one or more second models to relatethe first feature representation to the first latent representation maycomprise training a first model of the one or more second models todetermine a first mapping between the first feature representation andthe first latent representation, and training the one or more secondmodels to relate the second feature representation to the second latentrepresentation may comprise training a second model of the one or moresecond models to determine a second mapping between the second featurerepresentation and the second latent representation.

In some embodiments, the first model of the one or more second modelsand the second model of the one or more second models may be same model,and the first mapping and the second mapping may be a same mapping.

In some embodiments, training the one or more third models to relate thefirst latent representation to the mutual latent representation maycomprise training a first model of the one or more third models todetermine a first mapping between the first latent representation andthe mutual latent representation and training the one or more thirdmodels to relate the second latent representation to the mutual latentrepresentation may comprise training a second model of the one or morethird models to determine a second mapping between the second latentrepresentation and the mutual latent representation.

In some embodiments, the first model of the one or more third models andthe second model of the one or more third models may be a same model,and the first mapping and the second mapping may be a same mapping.

In some embodiments, the training process may further comprisereceiving, after training the set of models, a second training datasetincluding third values representing third signals output from a thirdchemical sensing unit and training a second set of models using thesecond training dataset and the trained set of models.

In some embodiments, training the second set of models using the secondtraining dataset and the trained set of models may comprise: training afifth model to relate the third values representing the third signals toa third feature representation; training a sixth model to relate thethird feature representation to a third latent representation; andtraining a seventh model to relate the third latent representation tothe mutual latent representation.

In some embodiments, training the sixth model to relate the thirdfeature representation to the third latent representation may comprisedetermining a mapping between the third feature representation and thethird latent representation using the first mapping, the second mapping,or a combination thereof.

In some embodiments, training the seventh model to relate the thirdlatent representation to the mutual latent representation may comprisedetermining a mapping between the third latent representation and themutual latent representation using the first mapping, the secondmapping, or a combination thereof.

In some embodiments, training the one or more first models to relate thefirst values representing the first signals to the first featurerepresentation may comprise determining a sequential relationshipbetween values of the first values; and training the one or more firstmodels to relate the second values representing the second signals tothe second feature representation may comprise training the one or morefirst models using the determined sequential relationship between valuesof the first values.

In some embodiments, training the one or more second models to relatethe first feature representation to the first latent representation maycomprise determining a sequential relationship between values in thefirst feature representation; and training the one or more second modelsto relate the second feature representation to the second latentrepresentation may comprise training the one or more second models usingthe determined sequential relationship between values in the firstfeature representation.

In some embodiments, training the one or more third models to relate thefirst latent representation to the mutual latent representation maycomprise determining a sequential relationship between values in thefirst latent representation; and training the one or more third modelsto relate the second latent representation to the mutual latentrepresentation may comprise training the one or more third models usingthe determined sequential relationship between values in the firstlatent representation.

In some embodiments, the fourth model may be configured to generateinferences based on a sequential relationship determined between valuesin the mutual latent representation.

In some embodiments, training the one or more first models may compriseusing a manifold learning technique, a neighborhood embedding technique,an unsupervised learning technique, or any combination thereof.

In some embodiments, the one or more second models may comprise neuralnetwork models.

In some embodiments, the neural network models may comprise feed forwardneural networks, recurrent neural networks, convolutional neuralnetworks, or any combination thereof.

In some embodiments, the one or more third models may comprise neuralnetwork models.

In some embodiments, the neural network models may comprise feed forwardneural networks, recurrent neural networks, convolutional neuralnetworks, or any combination thereof.

In some embodiments, the fourth model may comprise a feed forward neuralnetwork, a support vector machine, a recurrent neural network, orlong-short-term-memory neural network.

According to some embodiments, a method of training a set of modelsassociated with a first chemical sensing unit, using informationassociated with a plurality of chemical sensing units not including thefirst chemical sensing unit, is provided. The method may comprise:accessing the information associated with the plurality of chemicalsensing units, wherein the information relates a plurality of signalsoutput from the plurality of chemical sensing units to a mutual latentrepresentation; accessing a training dataset including valuesrepresenting signals output from the first chemical sensing unit; andtraining the set of models associated with the first chemical sensingunit, using the training dataset and the information associated with theplurality of chemical sensing units, wherein training the set of modelscomprises: (1) training a first model of the set of models to relate thevalues representing the signals output from the first chemical sensingunit to a feature representation; (2) training a second model of the setof models to relate the feature representation to a latentrepresentation; and (3) training a third model to relate the latentrepresentation to the mutual latent representation.

In some embodiments, the information associated with the plurality ofchemical sensing units may comprise at least one mapping between aplurality of latent representations associated with the plurality ofchemical sensing units, and the mutual latent representation.

In some embodiments, training the third model to relate the latentrepresentation to the mutual latent representation may comprisedetermining a mapping between the latent representation and the mutuallatent representation, using the at least one mapping between theplurality of latent representations and the mutual latentrepresentation.

In some embodiments, the determined mapping between the latentrepresentation and the mutual latent representation may comprise acombination of multiple mappings of the at least one mapping between theplurality of latent representations and the mutual latentrepresentation.

In some embodiments, the information associated with the plurality ofchemical sensing units may comprise at least one mapping between aplurality of feature representations associated with the plurality ofchemical sensing units, and the plurality of latent representationsassociated with the plurality of chemical sensing units.

In some embodiments, training the second model to relate the featurerepresentation to the latent representation may comprise determining amapping between the feature representation and the latentrepresentation, using the at least one mapping between the plurality offeature representations and the plurality of latent representations.

In some embodiments, determining the mapping between the featurerepresentation and the second latent representation may comprisecombining multiple mappings of the at least one mapping between theplurality of feature representations and the plurality of latentrepresentations.

In some embodiments, training the first model may comprise using amanifold learning technique, a neighborhood embedding technique, anunsupervised learning technique, or any combination thereof.

In some embodiments, the second models may comprise a neural networkmodel.

In some embodiments, the neural network model may comprise a feedforward neural network, a recurrent neural network, a convolutionalneural network, or any combination thereof.

In some embodiments, the third model may comprise a neural networkmodel.

In some embodiments, the neural network model may comprise a feedforward neural network, a recurrent neural network, a convolutionalneural network, or any combination thereof.

According to some embodiments, a system is provided comprising at leastone computer processor and at least one non-transitory computer-readablestorage medium storing processor-executable instructions that, whenexecuted by the at least one computer processor, may cause the at leastone computer processor to: access signals output from a chemical sensingunit having a plurality of sensors configured to sense at least oneanalyte in a sample, and generate an inference regarding the at leastone analyte in the sample using a set of models trained to relate thesignals to mutual latent representation values in a mutual latentrepresentation, wherein the mutual latent representation was generatedbased on signals output from a plurality of chemical sensing units.

In some embodiments, generating the inference regarding the at least oneanalyte in the sample may comprise generating feature representationvalues by providing the signals as input to a first model of the set ofmodels trained to relate the received signals to a featurerepresentation.

In some embodiments, generating the inference regarding the at least oneanalyte in the sample may comprise generating latent representationvalues by providing the feature representation values as input to asecond model of the set of models trained to relate the featurerepresentation to a latent representation.

In some embodiments, generating the inference regarding the at least oneanalyte in the sample may comprise generating the mutual latentrepresentation values by providing the latent representation values asinput to a third model trained to relate the latent representation tothe mutual latent representation.

In some embodiments, generating the inference regarding the at least oneanalyte in the sample may comprise generating the inference by providingthe mutual latent representation values as input to a fourth modeltrained to generate inferences based on the mutual latentrepresentation.

In some embodiments, any two or more models of the set of models may becombined into a single model.

In some embodiments, the signals may be output from a plurality ofchemical sensing units that output differing signals when exposed to asame analyte.

In some embodiments, the signals may be stored in the at least onenon-transitory computer-readable storage medium of the system.

In some embodiments, the at least one computer processor may access thesignals output from the chemical sensing unit by receiving the signalsdirectly from the chemical sensing unit.

In some embodiments, the signals may be stored in a storage mediumdifferent from and external to the at least one non-transitorycomputer-readable storage medium.

In some embodiments, wherein accessing the signals may comprisereceiving the signals from the storage medium.

In some embodiments, the chemical sensing unit may comprise the externalstorage medium.

In some embodiments, information representing at least a portion of theset of models may be stored in the at least one non-transitorycomputer-readable storage medium of the system.

In some embodiments, information representing at least a portion of theset of models may be stored in a storage medium different from andexternal to the at least one non-transitory computer-readable storagemedium.

In some embodiments, the information representing at least a portion ofthe set of models may be received from the at least one non-transitorystorage medium.

In some embodiments, the chemical sensing unit may include the at leastone non-transitory storage medium.

In some embodiments, the at least one computer processor may comprise aplurality of computer processors.

According to some embodiments, a chemical sensing system may be providedcomprising: (1) a plurality of chemical sensing units, each chemicalsensing unit of the plurality of chemical sensing units having aplurality of sensors arranged on at least one substrate, wherein a firstsensor and a second sensor of the plurality of sensors have differentsensitivities to sense at least one analyte in a sample, each of theplurality of sensors being configured to output a signal in response tosensing the at least one analyte; and (2) at least one computerprocessor programmed to receive the signals output from the plurality ofsensors for the plurality of chemical sensing units and determine aconcentration of the at least one analyte in the sample by: (i)providing the received signals as input to a first model trained torelate the signals to a feature representation to generate featurerepresentation values; (ii) providing the feature representation valuesas input to a second model trained to relate the feature representationto a latent representation to generate latent representation values;(iii) providing the latent representation values as input to a thirdmodel trained to relate the latent representation to a mutual latentrepresentation to generate mutual latent representation values; and (iv)providing the mutual latent representation values as input to a fourthmodel trained to related the mutual latent representation to analyteconcentrations to generate the concentration of the at least one analytein the sample.

The foregoing summary is provided by way of illustration and is notintended to be limiting. It should be appreciated that all combinationsof the foregoing concepts and additional concepts discussed in greaterdetail below (provided such concepts are not mutually inconsistent) arecontemplated as being part of the inventive subject matter disclosedherein. In particular, all combinations of claimed subject matterappearing at the end of this disclosure are contemplated as being partof the inventive subject matter disclosed herein.

BRIEF DESCRIPTION OF THE DRAWINGS

FIGS. 1A-1C depict components of an exemplary chemical sensing system.

FIG. 2A depicts an exemplary sequence of mappings from signals output bysensors of a single chemical sensing unit to an output representationhaving bases corresponding to relevant analytes.

FIG. 2B depicts a sequence of exemplary representations corresponding tothe mappings of FIG. 2A.

FIG. 3 depicts an exemplary process for training a set of models usingdata from multiple chemical sensing units.

FIG. 4 is a diagram depicting an exemplary set of models which may betrained according to the process of FIG. 3.

FIG. 5 is a diagram depicting an exemplary system architecture that maybe used when training models according to the techniques describedherein.

FIG. 6 depicts an exemplary process for training a set of models usingdata from previously trained models, and data from at least oneadditional chemical sensing unit.

FIG. 7 depicts an exemplary process for training a set of models usingsequential information about previously trained models, and data from atleast one additional chemical sensing unit.

FIG. 8 is a diagram depicting an exemplary set of models which may betrained according to the process of FIG. 7.

FIG. 9 is an exemplary process for using a trained set of models togenerate an inference based on input signals from a chemical sensingunit.

FIG. 10 is an exemplary process for using a trained set of models todetermine a concentration of an analyte in a sample based on inputsignals from a plurality of chemical sensing units.

FIGS. 11A-C depict graphic representations of exemplary latent andmutual latent spaces, according to some embodiments.

FIG. 12 depicts an illustrative implementation of a computer system thatmay be used in connection with some embodiments of the technologydescribed herein.

DETAILED DESCRIPTION

Chemical sensors are physical devices that exhibit a measurable responseto the presence of one or more chemical species. In a chemical sensorarray, multiple chemical sensors are operated in the context of the samesensing application. A chemical sensing unit may include a chemicalsensor array seated over a surface that will be exposed to chemicalfluids. In the presence of certain target chemicals, each chemicalsensor may make weak bonds with the chemical molecules, resulting in oneor more changes in chemo-physical characteristics of the sensor element,that are measurable via electronic analog signals. Compared to abiological olfactory system, the chemical sensors of a chemical sensingunit may mimic neural receptors, and the behavior of the signalsproduced by the chemical sensing unit may be similar to the output ofthe firing neurons.

The inventors have recognized and appreciated that, through thebiological evolution of organisms, the neural receptors within theolfactory system have developed to improve organisms' ability to survivein their environment, such as by finding food or detecting prey, findingpairs for reproduction, detecting threats like hunters, spoiled food,smoke of fire, and being aware of other factors that relate to anorganism's survival and that are associated with odors. The survivalinstinct in each organism has resulted in the evolution of neuralreceptors sensitive to specific odors. For example, in humans there areapproximately 400 genomes that produce different types of neuralreceptors that reside in the human nostril (as well as all over thebody) to detect odors, smells, and chemicals in the environment. Theneural receptors, once exposed to certain chemicals to which they aresensitive, make bonds with the chemicals and produce signals. Differentneural receptors may respond differently to the same chemical, due tothe diversity in the neural receptors, their topological distributionover the body, and the slight differences in the replication of the sametype of neural receptor. As a result, the neural receptors maycollectively contain information representing the chemicals present inthe organism's environment.

The inventors have recognized and appreciated that it may be desirableto provide a chemical sensing system that combines information obtainedfrom multiple chemical sensing units, in order to more fully representthe semantics (e.g., chemical characteristics) of the environment of thechemical sensing system and to thereby obtain more accurate and robustchemical sensing results. In general, some conventional chemical sensingsystems lack accuracy and/or robustness due to difficulties associatedwith effectively combining information obtained from multiple chemicalsensing units. A challenge faced by such conventional systems is thatvariations arising between multiple chemical sensing units may causedifferent chemical sensing units to have different responses (e.g.,output signals) when exposed to the same semantics (e.g., the chemicalconcentrations within an environment of the chemical sensing system overtime). These variations may be due, for example, to manufacturingdifferences between the sensing units and/or the decay over time of thechemical sensors within the chemical sensing units after repeatedlybeing exposed to chemicals.

The inventors have recognized and appreciated that some conventionalchemical sensing systems fail to effectively account for variationsbetween chemical sensing units, and therefore are unable to accuratelyextract information from and combine signals output by multiple chemicalsensing units. As a result, some conventional systems may be unable tomake accurate inferences about the corresponding semantics, or may do soonly with reduced time and/or cost efficiency of the chemical sensingsystem compared to a chemical sensing system that takes variations inchemical sensing units into account. Accordingly, the inventors havedeveloped techniques that provide improved chemical sensing systemscapable of efficiently and intelligently combining information frommultiple chemical sensing units.

Some embodiments relate to training one or more models (e.g. statisticalmodels, machine learning models, neural network models, etc.) to mapsignals output by a plurality of chemical sensing units of a chemicalsensing system to a common representation space that at least partiallyaccounts for differences in signals output by the different chemicalsensing units. Following training of the one or more models, new signalssubsequently obtained from the chemical sensing units of the chemicalsensing system may be provided as input to the trained model(s) toproduce corresponding values in the common representation space. Basedon these values, the chemical sensing system may generate an inference(e.g., an identification, quantification, or description) regarding thecorresponding semantics (e.g., chemical characteristics) of itsenvironment.

In general, training models, such as those described herein, may requiresignificant quantities of training data (e.g., output signals from anumber of chemical sensing units) to be able to accurately characterizethe chemical composition of an environment in which a chemical sensingsystem is placed. However, obtaining such training data can be atime-consuming and resource-intensive process. For example, obtainingtraining data may require a user or manufacturer of a chemical sensingsystem to perform repeated experiments with the chemical sensing units.These experiments may involve exposing the chemical sensing units to avariety of semantics, which may include a wide range ofapplication-specific semantics, and recording the corresponding outputsignals from the chemical sensing units. In some instances, it may bedesirable to train the model(s) associated with the chemical sensingsystem using a smaller training data set, thereby reducing the time andeffort associated with training.

Some embodiments relate to techniques for reducing the amount oftraining data needed to integrate an additional chemical sensing unitinto an existing chemical sensing system. These techniques may bereferred to herein as “semi-supervised training” or “training with weaksupervision.” As described herein, these techniques may involve usinginformation about previously-trained model(s) associated with theexisting chemical sensing system to provide partial supervision of atraining process for the additional chemical sensing unit. Inparticular, as part of training one or more additional models associatedwith the additional chemical sensing unit, a reduced quantity oftraining data may be utilized in combination with information about thepreviously-trained models, such that the additional model(s) attain anacceptable accuracy (e.g., an accuracy above a certain threshold, suchas 80% accuracy). For instances, only a small fraction of the trainingdata that would be required to train the additional model(s) without theinformation about the previously-trained models (e.g., less than 10% ofthe training data, such as 5% or 2% of the training data) may be used toobtain a desired model accuracy.

A chemical sensing unit designed in accordance with some embodiments mayoperate in a manner akin to olfaction in biological systems. To detectsmells of interest and the smell strength in an environment, eachindividual chemical sensor of the chemical sensing unit may be designedto respond to one or more functional chemistry groups of interest,corresponding to the smells of interest. The smells of interest may beselected, for example, as part of a particular application for whichonly certain smells may be of relevance (e.g., detecting smoke, rottingfood, or other phenomena associated with certain odors). In general, theenvironment of a chemical sensing system may be a volume, referred toherein as a headspace, in which the chemical sensing system resides.

A chemical sensor can be operated in an environment that includes one ormore chemical species. At least one of the chemical species in theenvironment may be present in a fluid form (e.g., in a liquid phaseand/or a gas phase). A chemical sensor may be sensitive to the presenceof some molecules at a variety of concentrations, but may not besensitive to others. A chemo-physical response of a sensor to variouschemical species may take the form of signals output at measurablelevels. The concentration of the chemical species in the environment maybe quantified as a scalar value in conjunction with a chosen unit ofmeasurement. For example, the concentration of gaseous methane in aircan be quantified in terms of molar concentration.

A sensor can be configured to sense a concentration of one or morerelevant chemical species (referred to herein as analytes) in theenvironment. The concentration of analytes in the environment isreferred to herein as the composition of the environment. For example, acarbon monoxide detector can be configured to sense a concentration ofcarbon monoxide present in an environment also including other chemicalspecies (e.g., oxygen and nitrogen). When a sensor array is configuredto detect M analytes, a unit of measurement defines an M-dimensionalvector space isomorphic to R^(M). The elements in the vector spaceuniquely describe a composition of the environment. The composition ofthe environment as measured by a sensor may depend on a location of thesensor and may vary over time.

FIG. 1A and FIG. 1B depict views of an exemplary chemical sensing unit100. Chemical sensing unit 100 includes a sensor array 120. Individualsensor outputs from a plurality of sensors in the array may exhibitincomplete information about the chemical species in the environment inwhich the chemical sensing unit is placed. For example, each sensoroutput may exhibit a dependence on multiple, time varying extraneousvariables (e.g., temperature, humidity, etc.) that are not wellspecified based on the output of that sensor alone. By includingmultiple sensors in an array, the chemical sensing unit may beconfigured to estimate the chemical composition of an environment usingmultiple output signals generated by the multiple sensors in the array.As described in more detail below, some embodiments process the outputfrom multiple sensors in an array using an inferential model to generatean estimate of a concentration of one or more chemical species in theenvironment.

Chemical sensing unit 100 includes a base 110 configured to support asensor array 120. Base 110 may be implemented using any suitablesubstrate including, but not limited to, a circuit board. The sensorarray 120 includes a plurality of sensors (e.g., sensor 121). Thesensors may be arranged in rows and columns, as shown, or the sensorsmay be arranged in another arrangement (e.g., concentric circles,staggered rows, etc.). The described location and orientation of thesensors on chemical sensing unit 100 are not intended to be limiting.

Chemical sensing unit 100 includes a controller 130. In someembodiments, controller 130 is configured to provide power to theplurality of sensors. In some embodiments, controller 130 is configuredto acquire signals from the plurality of sensors. For example, each ofthe sensors may include, or be a part of, a Wheatstone bridge or anothercircuit configured to measure changes in resistance. Controller 130 maybe configured to provide power for the sensors and/or acquire signalsfrom the sensors corresponding to changes in resistance measured by thesensors. In some embodiments, controller 130 is further configured toprovide one or more of signal conditioning, signal processing, andsignal communication. For example, controller 130 may be configured tofilter and amplify signals received from the sensors. In someembodiments, controller 130 is further configured to perform at leastsome of the mapping operations described in more detail below. Forexample, controller 130 may be configured to implement one or moremodels relating the signals output by the sensors to a latentrepresentation, or to an output representation having one or more axescorresponding to relevant analytes. In some embodiments, controller 130includes at least one storage device (e.g., a memory) configured tostore parameters that define one or more of the mapping operations,described in more detail below.

Chemical sensing unit 100 includes a communications component 140, whichcan include hardware and/or software configured to enable chemicalsensing unit 100 to communicate with other elements of the chemicalsensing unit (or other devices). For example, communications component140 may include a network controller configured to provide local areanetwork connectivity, a port controller configured to provide parallelport and/or serial port connectivity, and/or a wireless controllerconfigured to provide WIFI, BLUETOOTH, ZIGBEE or similar connectivity.

In accordance with some embodiments, a sensor (e.g., sensor 121)includes a substrate 122 and one or more electrodes (e.g., electrodes123 a and 123 b) disposed on substrate 122. In one implementation ofsensor 121, a conductive thin film 124 is disposed on and betweenelectrodes 123 a and electrodes 123 b as shown. For example, thin film124 can include conductive nanoparticles. In some embodiments, thin film124 is chemically sensitive. For example, thin film 124 may undergo aphysical change (e.g., swelling, contracting, and/or a change incomposition or state) upon exposure to an analyte. The physical changein the thin film 124 may result in a change in resistance betweenelectrode 123 a and electrode 123 b. Controller 130 may be configured tomonitor the resistance between electrode 123 a and electrode 123 b,resulting in an output signal from the sensor that is detectable bycontroller 130. The output signal may include semantic informationconcerning one or more analytes introduced to the sensor.

In some embodiments, one or more of the sensors in sensor array 120 areconfigured with differing sensitivities to different analytes. Forexample, thin films for different sensors in the array may be configuredto provide different degrees of physical change in response to exposureto the same analyte. As an additional example, a thin film for a sensorcan be configured to provide different degrees of physical change inresponse to exposure to different analytes. Accordingly, in someembodiments, the output signals from different sensors in the array maydiffer in the presence of the same analyte and/or the output signal fromthe same sensor may differ in the presence of different analytes in theenvironment. These differences may include, but are not limited to,differences in amplitude and/or temporal characteristics of the outputsignal.

FIG. 1C depicts an exemplary chemical sensing system 150, which mayinclude chemical sensing units 100 and, optionally, an external storagemedium 190. Each of the chemical sensing units 100 may be designed inthe manner described herein at least with respect to FIGS. 1A-B. Asdepicted in the figure, the chemical sensing units 100 of chemicalsensing system 150 may be capable of communicating with one another,such as by using the communications component 140 included in eachchemical sensing unit, or any other suitable channel of communication.This communication channel may be utilized to share information such astraining data, model information, or output signals between the chemicalsensing units 100. For a given chemical sensing unit 100, the sharedinformation may be stored, for example, on a storage device associatedwith the controller 130 of the chemical sensing unit or on externalstorage medium 190.

As shown in FIG. 1C, external storage medium 190 may be accessible bythe chemical sensing units 100 via their communications components 140.The external storage medium 190 need not be a single storage device, butmay be distributed over a number of devices, such as in a cloud storageconfiguration. In some cases, one or more of the chemical sensing units100 may store information such as training data, model information, oroutput signals on the external storage medium 190. One or more of thechemical sensing units 100 may also access information from the externalstorage medium 190, not limited to information stored by the chemicalsensing units on the external storage medium, including training data,model information, output signals, or other information.

Similar to neural receptors, which may produce signals that undergofurther processing in the central nervous system, chemical sensorsincluded in some embodiments may produce signals, at least some of whichare subsequently transformed via one or more functions. FIG. 2A depictsan exemplary process 200 of mapping signals output by sensors (e.g., thesensors of a chemical sensing unit 100) to an output representationhaving bases corresponding to relevant analytes (e.g., an M-dimensionalvector space V, having elements {right arrow over (v)}, as describedherein). Note that the process 200 of FIG. 2A includes steps which neednot be performed in all embodiments. For example, in some embodiments,the process 200 may end at block 230, or at any other step in process200, and may thereafter proceed with a process as described herein atleast with respect to FIGS. 3 and 4.

FIG. 2B depicts a sequence of exemplary representations (also referredto herein as models or sub-models) corresponding to the mappings of FIG.2A. As discussed with respect to FIG. 2A, not all the representationsdepicted in FIG. 2B need be used in every embodiment. Instead, in someembodiments, only some of the depicted representations may be utilized(e.g., feature representation 221 and latent representation 231) and,thereafter, alternative representations and maps may be used, such asthose described herein at least with respect to FIGS. 3 and 4.

Returning to FIG. 2A, the exemplary process 200 begins at operation 210,where chemical sensors produce output signals. In general, the process200 can operate on input data (e.g., datasets, streaming data, files, orthe like) in a variety of formats, such as divided into semanticallyseparate partitions corresponding to different environmental andoperational contexts. For example, the input data may be divided intomultiple datasets, data streams, files, etc. corresponding to differentsensors, times, contexts, environments, or the like. Such partitions maycontain multiple input data entries, one input data entry, or no inputdata entries. Under such partitioning, the datasets and data streams maybe viewed as composites of the individual semantic partitions, and theanalyses applied to the datasets and data streams may be equivalentlyapplied to semantic partitions and vice-versa.

As described herein, the input data may include output signals obtainedfrom sensors (e.g., raw data output from the sensors) and/or dataderived from the signals output from the sensors (e.g., one or morefeatures extracted from the output signals). In some aspects, the outputsignals obtained from the sensors may be filtered to reduce noise in theoutput signals. Any suitable filtering technique may be used dependingon the nature of the sensor response and the noise present in the outputsignals. Unless otherwise specified, the output signals described hereinmay be either filtered output signals or non-filtered output signals. Insome embodiments, the input data includes time values. For example, theinput data may include timestamps corresponding to output signal values.In some embodiments, time values may be implicitly determined from thedata. For example, the input data may include an initial timestamp and asampling frequency such that time values for input data following theinitial timestamp may be determined based on the initial timestamp andthe sampling frequency.

In some embodiments, the input data can include concentrationinformation corresponding to the output signals. When the input datalacks concentration information for all of the relevant analytes, theinput data is referred to herein as “unlabeled data.” When the inputdata lacks concentration information for some of the relevant analytes,the input data is referred to herein “partially labeled data.” When theinput data includes concentration information for all of the relevantanalytes, the input data is referred to herein as “labeled data.” Insome embodiments, the input data includes contextual information. Thecontextual information may include, for example, information about theenvironment of the device such as the temperature of the environment,the application the system is employed in, explicit information aboutthe presence or absence of irrelevant analytes, or other contextualinformation relating to the operation of the sensor array.

In some embodiments, process 200 is implemented by sequentially applyingone or more models to the data. The one or more models may includeparameters and hyper-parameters stored in a memory component of thechemical sensing system. In some embodiments, the parameters are learnedusing machine learning techniques, examples of which are described inmore detail below. A chemical sensing system configured to apply thesequence of one or more models according to the learned parameters andhyper-parameters to output signals may infer a chemical composition ofan environment from the output signals.

A sequence of models that collectively map the input data to the outputrepresentation (e.g., the vector space V) may be generated in place of asingle model that performs the same function. Using a sequence of modelsmay improve the flexibility of the chemical sensing system. Furthermore,the effect of each individual model may be more easily reviewed and/orinterpreted when using a sequence of models that collectively map theinput data to the output representation, allowing for convenientadjustment or debugging of individual models.

In some embodiments, the sequence of models may include a first modelthat relates the output signals to an intermediate representation (e.g.,a feature representation, latent representation, or straightenedorthogonal representation, as described herein) and a second model thatrelates the intermediate representation to the output representation.Different versions of the first model may be specific to differentimplementations or instances of chemical sensing unit 100. Similarly,different versions of the second model may relate the intermediaterepresentation to different output representations. Depending on thechemical sensing system and the desired output representation, anappropriate version of the first model may be used together with theappropriate version of the second model. The two models may be generatedseparately (e.g., at different times or locations, or by differentdevices), or applied separately.

As one example, a first chemical sensing system can apply the firstmodel to the output signals to generate the intermediate representation.A second chemical sensing system can subsequently apply the second modelto the intermediate representation to generate the outputrepresentation. In some embodiments, the first model can be specific tothe first device. Thus, a first device-specific model can be trained tomap input data acquired by the first device to the intermediaterepresentation. The first device-specific model can subsequently be usedto specify initial parameters for training additional device-specificmodels. For example, when training a second device-specific model for asecond device, at least some of the parameters of the seconddevice-specific model can be initialized to at least some of theparameters of the first device-specific model. In some embodiments, thesecond model can be trained independent of any particular device. Forexample, when the second model is implemented as a device-independentmodel, it can be trained to map input data from intermediaterepresentations generated by one or more device-specific models to theoutput representation.

In some embodiments, one or both of first and second models includes atleast two sub-models, each of which divides the mapping for a model intomultiple sub-mappings which may undergo a separate learning process. Forexample, in some embodiments, the second model is divided into a firstsub-model relating the feature representation output from the firstmodel to a latent representation, a second sub-model relating a latentrepresentation to a straightened orthogonal representation, and a thirdsub-model relating a straightened orthogonal representation to theoutput representation.

The composition and training of the models and/or sub-models used inaccordance with some embodiments, are described in more detail below. Insome embodiments, one or more of the models or sub-models are trainedusing parametric techniques, such as support vector machines, randomforests, or deep neural networks. In other embodiments, one or more ofthe models or sub-models are trained using non-parametric techniques,such as t-distributed stochastic neighbor embedding (t-SNE), uniformmanifold approximation and projection (UMAP), or k-nearest neighborstechniques (k-NN).

For convenience, FIGS. 2A and 2B are described with regard to tuples ofthe form {D(t_(i))=(t_(i), C(t_(i)), {right arrow over (x)}(t_(i)),{right arrow over (a)}(t_(i)))}, where t_(i) is a unique timestamp,{right arrow over (x)}(t)=

(x₁(t), . . . , x_(N)(t)

is the response of a sensor array including N sensors at time t_(i), and{right arrow over (a)}(t_(i)) may be the corresponding vector ofconcentrations of relevant analytes. As described above, {right arrowover (x)}(t) may represent a filtered version of the output signals fromthe sensors to reduce noise in the output signals. When informationabout the concentration of a relevant analyte is not available, thecorresponding elements of {right arrow over (a)}(t_(i)) may include anelement (a “null element”) indicating the unavailability of suchinformation (e.g., a default value, a NaN, or the like). For example,when no information about the concentration of relevant analytes isavailable, {right arrow over (a)}(t_(i)) may be a vector of nullelements. As used herein, a data entry D(t_(i)) is referred to as“unlabeled” when all elements of {right arrow over (a)}(t_(i)) are nullelements, partially labelled when some but not all elements of {rightarrow over (a)}(t_(i)) are null elements, and D(t_(i)) is referred to as“labelled” when none of the elements of {right arrow over (a)}(t_(i))are null elements. C(t_(i)) may include a vector of contextualinformation, such as the contextual information described above.However, the disclosed embodiments are not limited to tuples of the form{D(t_(i))=(t_(i), C(t_(i)), {right arrow over (x)}(t_(i)), {right arrowover (a)}(t_(i)))}.

In operation 210, chemical sensors (e.g., sensors in sensor array 120)of a sensing device (e.g., chemical sensing unit 100) may transduce achemical signal 3 dependent on the composition of the environment intoelectrical output signals {right arrow over (x)}(t) (e.g., from chemicalsensing unit 100 to output signals 211, as depicted in FIG. 2B). In someembodiments, the values of output signals 211 may reflect changes in thecomposition of the environment over time. In some embodiments, theseoutput signals may include transient changes in value in response to achange in the composition of the environment. For example, a baselinevalue prior to the change in the composition of the environment may beapproximately the same as a steady-state value reached after the changein the composition of the environment. In various embodiments, theseoutput signals may reach a new steady-state value dependent on thechanged composition of the environment.

According to some embodiments, the chemical sensors produce signals thatmay be transformed via one or more functions into tuples of numbers thatprovide a feature representation of the composition of the environment.Such a feature representation may be considered a numeric representationof the odor semantics associated with certain mixtures of chemicals. Insome cases, odor semantics may involve changes of odors in a sequence;for example, the odor of a food recipe given a sequence of the odorsproduced during the cooking process. In accordance with the design anddevelopment of chemical sensors, a feature representation may containinformation that identifies and/or quantifies the smells in theenvironment of a chemical sensing unit. As described herein, a featurerepresentation may be produced in order to interpret the chemicalcomposition of the gasses in the environment of the chemical sensingunit.

In operation 220, the output signals are applied to a model that relatesoutput signals to a feature representation (e.g., a mapping from outputsignals 211 to feature representation 221, as depicted in FIG. 2B) togenerate feature vectors corresponding to the output signals. In thismanner, the model may de-convolve relevant information from the outputsignals. The relationship established by the model can be expressed, foran output signal x_(i)(t), as a map to a feature representation, ζ_(i):

^(T) ^(i) →

^(K) ^(i) , where T_(i) denotes some (possibly infinitely large) numberof samples that span some time interval [t_(i), t_(T) _(i) ], and K_(i)denotes a number of features extracted from the output signal. Such amap produces a feature vector, {right arrow over(z_(j))}=ζ_(i)(x_(i)[t_(i), t_(T) _(i) ])), where {right arrow over(z_(j))}∈

^(K) ^(i) . As discussed herein, i may be expressed as a parametricfunction of some parameter set θ_(i): {right arrow over(z_(j))}=ζ_(i)(x_(i)([t₁, t_(T) _(i) ]); θ_(i)). Values for theseparameters may be estimated using, for example, machine learningtechniques such as feedforward neural networks and Gaussian processes.

In some embodiments, the number of maps ζ_(i) may not equal the numberof output signals x_(i)(t). For example, features may not be extractedfrom some output signals (resulting in fewer maps), or features may beextracted from combinations of output signals in addition to individualoutput signals (resulting in additional maps). In general, when thenumber of output signals is N, the number of maps ζ_(i) will be equal toN′. The result of applying ζ={ζ₁, . . . , ζ_(N′)} to {right arrow over(x)}(t) may be expressed as a composite feature vector {right arrow over(z)}=

z₁, . . . , z_(N′)

, where {right arrow over (z)}∈

∈R^(K), and K=Σ_(i) K_(i) is the collection of features extracted fromall maps comprising ζ. As used herein, such a composite feature vectoris referred to as a feature vector. For {right arrow over (z)} asdefined above, let the span of all possible feature vectors {right arrowover (z)} be denoted as the feature space Z, where Z⊆

^(K).

In some embodiments, N may be a large number, and K may be larger thanN. As such, numerical methods applied in Z may suffer from the curse ofdimensionality. Furthermore, a change in concentration Δ{right arrowover (v)} may yield a non-linear change Δ{right arrow over (z)} in thefeature vector, which may, in some cases, preclude the use of lineardimensionality reduction techniques.

In some embodiments, properties of the feature space Z may be used toassociate feature vectors with analytes, without relying on vectors ofconcentrations of relevant analytes (e.g., without relying on {rightarrow over (a)}(t_(i))). These associations may be used to train modelsthat implement mappings imposing straightness and orthogonalityconditions on the data. For example, an association can be createdbetween feature vectors corresponding to varying concentrations of thesame analyte. A model can be generated, using this association, thatimplements a mapping to a representation in which points correspondingto the feature vectors are aligned along a single vector. As anadditional example, a first association can be created between firstfeature vectors corresponding to varying concentrations of a firstanalyte and a second association can be created between second featurevectors corresponding to varying concentrations of a second analyte. Amodel can be generated, using the first and second associations, thatimplements a mapping to a representation in which first pointscorresponding to the first feature vectors are aligned along a firstvector, second points corresponding to the second feature vectors arealigned along a second vector, and the first vector and second vectorare orthogonal.

In some embodiments, an iterative process is used to identify featurevectors corresponding to varying concentrations of a single analyte.This process can be performed automatically (e.g., without userdirection or input). This approach assumes that feature vectorscorresponding to varying concentrations of a single analyte are on theoutside, or hull, of manifold Z′. Points in Z′ corresponding tocombinations of two or more analytes may lie between these exteriorpoints, either on the hull of manifold Z′ or in the interior of manifoldZ′. A sequence of samples including a fixed concentration of a firstanalyte and decreasing concentrations of a second analyte approach alocation in Z′ corresponding to the fixed concentration of a firstanalyte along a first trajectory. A sequence of samples including thefixed concentration of the first analyte and decreasing concentrationsof a third analyte approach the location in Z′ corresponding to thefixed concentration of the first analyte along a second trajectory,distinct from the first trajectory. Thus, points corresponding tovarying concentrations of a single analyte can be identified as pointson the hull of manifold Z′ where trajectories defined by neighboringpoints change (e.g., locations with local gradient changes). Thefollowing iterative process may be used to identify such points.

As a first step, a space D is initialized to equal space Z and includesall of the points in space Z. A point z₁ in D is selected. Another pointz₂ in a neighborhood of z₁ is selected and a vector {right arrow over(z₁z₂)} is created. A sequence of points is then identified, each pointin the sequence in a neighborhood of the preceding point in the sequencesatisfying a directionality criterion with respect to {right arrow over(z₁z₂)}. Satisfaction of this directionality criterion may indicate thata point is sufficiently aligned with the vector {right arrow over(z₁z₂)}. In some embodiments, the directionality criterion may depend ona vector between the preceding point in the sequence and the currentpoint in the sequence. For example, the directionality criterion maydepend on a cosine value of the angle between {right arrow over (z₁z₂)}and the vector. When the cosine value is less than a threshold, thedirectionality criterion may not be satisfied. For example, a firstpoint z₃ in the sequence may be in a neighborhood of z₂ and may satisfythe directionality criterion when a cosine value of the angle between{right arrow over (z₁z₂)} and {right arrow over (z₁z₃)} is greater thana threshold. In various embodiments, the directionality criterion maydepend on a distance from the next point in the sequence to a projectionof the vector {right arrow over (z₁z₂)}. The sequence may end when nofurther point can be identified along this direction. Additionalsequences can be generated in this fashion for all points z₁ in Z and z₂in the neighborhood of z₁. The set of final points E for all of thesequences may then define a boundary space in D. The space D can beupdated to include only the boundary points E. The process ofidentifying boundary points can then be repeated to generate a new setof final points E.

This process can be repeated until E comprises a set of one-dimensionalmanifolds that cross an origin corresponding to an absence of a sensorresponse. Each of these one-dimensional manifolds comprises featurevectors corresponding to pure chemicals or base analytes. By applyingthis process, feature vectors can be associated with one-dimensionalmanifolds correspondent to the base analytes. This association can thenbe used to perform unsupervised learning in operations 241 and 251,without relying on labels for the samples. In semi-supervisedtechniques, partial availability of labels indicating concentrationsassociated with feature vectors can help validate the formation of eachmap and space by comparing a label for a sample with a positioncorresponding to the sample in each space. Partial labels can also beused to label an axis corresponding to base analytes. For example, whena sample lies on or near an axis and a label for the sample indicatesconcentrations of analytes, the axis can be labeled as corresponding tothe analyte having the greatest concentration.

In some embodiments, {right arrow over (x)}(t) may be continuous withrespect to changes in {right arrow over (v)}(t). Mapping may be selectedso as to preserve the continuity of Δ{right arrow over (z)}(t) withrespect to Δ{right arrow over (v)}(t). When the output signal {rightarrow over (x)}(t) is unique for each chemical composition of theenvironment {right arrow over (v)}(t), and ζ is selected to preserveuniqueness of {right arrow over (z)} with respect to {right arrow over(v)}, then there exists a one-to-one mapping H⁻¹ between the exemplaryoutput representation V and Z′ where the image V defines a continuousmanifold Z′⊆Z as depicted in FIG. 2B.

When exemplary output representation V and Z′ are open sets, theone-to-one mapping H⁻¹ is a homeomorphism. By definition, ahomeomorphism H then exists between Z′ and V. In such instances, Z′comprises a manifold of dimension M embedded in Z (as depicted infeature space 221 of FIG. 2B). Furthermore, each dimension of V maps toa one-dimensional, potentially non-linear manifold embedded in Z′. Themapping Ω from Z′ and V may thus be decomposed into sub-mappings. Asdescribed above, sub-models may implement these sub-mappings. Suchsub-models may be easier to generate than a model that implements H, andmay provide additional flexibility to the chemical sensing system.

In operation 230, the feature vectors generated in operation 220 can beapplied to a first sub-model that relates the feature representation Zto a latent representation Φ (e.g., from feature representation 221 tolatent representation 231, as depicted in FIG. 2B) to generate latentvalue vectors corresponding to the feature vectors. In some embodiments,the latent representation Φ can be an inner product space. The latentrepresentation Φ can be of the same dimension as the manifold Z′. As anon-limiting example, when Z′ is a plane embedded in Z, then the latentrepresentation Φ may be a two-dimensional space (e.g., latentrepresentation 231, as depicted in FIG. 2B). The first sub-model mayimplement a mapping φ: Z→Φ. Such a map may produce a latent value vector{right arrow over (p)}=φ({right arrow over (z)}), where {right arrowover (p)}∈

^(dim(z′)). In some embodiments, when Z′ is not embedded in Z, φ mayreduce to the identity function. As discussed herein, φ may be expressedas a parametric function of some parameter set Λ: {right arrow over(p)}=φ({right arrow over (z)}; Λ). Values for parameter set Λ may beestimated using machine learning techniques such as feedforward neuralnetworks and Gaussian processes. In some embodiments, the mapping φ: Z→Φfulfills the following conditions: φ is a continuous mapping between Z′and Φ, φ is bijective from Z′ to Φ, φ⁻¹ is a continuous mapping betweenΦ and Z′, and φ⁻¹ is bijective from Φ and Z′. The above conditions mayfollow from the homeomorphism between Z′ and Φ.

In operations 240 and 250, the latent value vectors generated inoperation 230 can be applied to a second sub-model that relates thelatent representation Φ to a straightened, orthogonalized representationΩ. In some embodiments, this second sub-model includes two componentmodels. As described above, multiple component models may provide moreflexibility and be more easily interpreted than a single model providingthe same functionality.

In operation 240, the latent value vectors generated in operation 230can be applied to the first component model to generate aligned vectorscorresponding to the latent value vectors (e.g., from latentrepresentation 231 to straightened representation 241, as depicted inFIG. 2B). The first component model may relate latent representation Φto straightened representation Ψ. In latent representation Φ, samplesincluding varying concentrations of a single analyte may be described bya non-linear, one-dimensional manifold. The first component model mayimplement a mapping ψ: Φ→Ψ that maps each such manifold to astraightened non-linear, one-dimensional manifold in Ψ. For example, twodiffering concentrations of the same analyte (e.g., {right arrow over(v₂)}=c{right arrow over (v₁)}, {right arrow over (v₁)}, {right arrowover (v₂)}∈V, c∈

) may map to two latent value vectors (e.g., {right arrow over (p₁)},{right arrow over (p₂)}∈Φ). Mapping ψ may map {right arrow over (p₁)}and {right arrow over (p₂)} to {right arrow over (s₁)}, {right arrowover (s₂)}∈Ψ such that an angle between {right arrow over (s₁)} and{right arrow over (s₂)} is minimized. For example, ψ may be determinedsuch that cosine distance d({right arrow over (s₁)}, {right arrow over(s₂)}) is maximized. When the manifolds in Φ are already straight, ψ mayreduce to the identity function. As discussed herein, ψ may be expressedas a parametric function of some parameter set Σ: {right arrow over(s)}=ψ({right arrow over (p)};Σ). Values for parameter set Σ may beestimated using machine learning techniques, such as feedforward neuralnetworks and Gaussian processes. In some embodiments, the mapping ψ: Φ−Ψfulfills the following conditions: ψ is a continuous mapping between Φand Ψ, ψ is bijective from Φ to Ψ, ψ⁻¹ is a continuous mapping between Ψand Φ, and ψ⁻¹ is bijective from Ψ to Φ. The above conditions may followfrom the homeomorphism between Ψ and Φ. Furthermore, function ψ mayreduce the impact of noisy data, as ψ may align latent value vectors inΦ corresponding to noisy measurements of the same analyte along the samedirection in Ψ.

In operation 250, the latent value vectors generated in operation 230can be applied to the second component model to generate independentvectors corresponding to the aligned vectors (e.g., from straightenedrepresentation 241 to orthogonal, straightened representation 251, asdepicted in FIG. 2B). The second component model may relate straightenedrepresentation Ψ to straightened, orthogonal representation Ω. Instraightened representation Ψ, varying concentrations of the sameanalyte may map to a straightened, non-linear, one-dimensional manifold(e.g., straightened representation 241, as depicted in FIG. 2B). Thesecond component model may implement a mapping ω: ψ→Ω that maps suchmanifolds to orthogonal, straightened non-linear, one-dimensionalmanifolds in Ψ. For example, two samples of two different analytes(e.g., {right arrow over (v₂)}⊥{right arrow over (v₁)}, {right arrowover (v₁)}, {right arrow over (v₂)}∈V) may map to two independentvectors (e.g., {right arrow over (s₁)}, {right arrow over (s₂)}∈Ψ).Mapping w may map {right arrow over (s₁)} and {right arrow over (s₂)} to{right arrow over (q₁)}, {right arrow over (q₂)}∈Ω such that an anglebetween {right arrow over (q₁)} and {right arrow over (q₂)} ismaximized. For example, Ω may be determined such that cosine distance d({right arrow over (q₁)}, {right arrow over (q₂)}) is minimized. Whenthe manifolds corresponding to the different analytes in ψ are alreadyorthogonal, ω may reduce to the identity function. As discussed herein,ω may be expressed as a parametric function of some parameter set Y:{right arrow over (q)}=ω({right arrow over (s)}; Y). Values forparameter set Y may be estimated using machine learning techniques, suchas feedforward neural networks and Gaussian processes. In someembodiments, the mapping ω: Ψ→Ω fulfills the following conditions: ω isa continuous mapping between ψ and Ω, ω is bijective from Φ to Ω, ω⁻¹ isa continuous mapping between Ω and Ψ, and ω⁻¹ is bijective from Ω to Ψ.The above conditions may follow from the homeomorphism between Ω and Ψ.Furthermore, function w may reduce the impact of noisy data, as w maymap aligned vectors in Ω corresponding to noisy measurements ofdifferent analyte along orthogonal directions in Ψ.

In operations 260 and 270, the independent, aligned vectors generated inoperation 250 can be applied to a third sub-model that relates theorthogonal, straightened representation Ω to the output representationV. In some embodiments, this third sub-model can include two componentmodels. As described above, multiple component models may provide moreflexibility and be easier to train than a single model providing thesame functionality.

In operation 260, the first component model can be configured to alignthe orthogonal, straightened manifolds corresponding to varyingconcentrations of differing analytes with the standard basis vectors of

^(M) (e.g., from orthogonal, straightened representation 251 to standardbasis representation 261, as depicted in FIG. 2B). For example, thefirst component model can be configured to implement a mapping τ: Ω→Uthat maps manifolds corresponding to varying concentrations of a singlebase analyte to the standard basis vectors e_(i) of

^(M). For example, when the chemical sensing unit is configured todetect two analytes, samples including varying concentrations of a firstanalyte can lie on a first one-dimensional, straightened manifold in Ω.Samples including varying concentrations of the second analyte can lieon a second one-dimensional, straightened manifold in Ω, orthogonal tothe first one-dimensional, straightened manifold. In thistwo-dimensional example, the first component model can map the firstone-dimensional, straightened manifold to the standard basis vectore₁=[1 0] and map the second one-dimensional, straightened manifold tothe standard basis vector e₂=[0 1]. When the chemical unit is configuredto detect additional relevant analytes, the representation Ω willcontain more manifolds corresponding to these additional relevantanalytes, which will be mapped to additional standard basis vectorse_(i) of

^(M). As discussed herein, T may be expressed as a parametric functionof some parameter set Π: {right arrow over (u)}=τ({right arrow over(q)}; Π). Values for parameter set H may be estimated using machinelearning techniques, such as feedforward neural networks and Gaussianprocesses. In some embodiments, τ may comprise one or more rotationmatrices. The parameters comprising parameter set Π may be values in theone or more rotation matrices.

In operation 270, the second component model can be configured to mapfrom the manifolds corresponding to single analytes in U to linearizedmanifolds corresponding to single analytes in V (e.g., from standardbasis representation 261 to output representation 271, as depicted inFIG. 2B). In some embodiments, for example, doubling a concentration ofan analyte in the environment may not result in a doubling of acorresponding value in U. Accordingly, the first component model can beconfigured to implement a mapping η: U→V that maps the standard basisrepresentation U to output representation V. The relationship betweenconcentrations of analytes in the environment and values in outputrepresentation V may be linear. For example, a doubling of aconcentration of an analyte in the environment may result in a doublingof a corresponding value in V. As discussed herein, η may be expressedas a parametric function of some parameter set Γ: {right arrow over(v)}=η({right arrow over (u)};Γ). Values for parameter set Γ may beestimated using machine learning methods, such as feedforward neuralnetworks and Gaussian processes.

The above described process 200 is intended to be exemplary andnon-limiting. In some embodiments, one or more acts of process 200 maybe omitted. For example, act 230 may be omitted when the Z′ is notembedded in Z. As an additional example, acts 240 and 250 may be omittedwhen the one-dimensional manifolds corresponding to the varyingconcentrations of single analytes do not require straightening ororthogonalization. Furthermore, the association of one-dimensionalmanifolds in Ω with analytes and the generation of output representationV can be combined into a single act. In this single act, each element ofV may be described by a unique directional vector ŝ_(k) in Ψ. Thecollection of M vectors ŝ_(k) may define a basis for Ψ. This basis maybe orthogonalized and transformed to the standard basis of

^(M) using, standard linear algebra techniques, and described by thelinear transformation {right arrow over (u)}=G{right arrow over (s)}.This linear transformation may be more generally denoted as a parametricfunction of G: {right arrow over (u)}=ρ({right arrow over (s)}, G). Inthe case where the vectors ŝ_(k) already form an orthogonal basis, Greduces to the identity function. Under the linear transformation G, thevector û_(k)=Gŝ_(k) becomes a scalar multiple of a standard basis vectorê_(k), and {right arrow over (v)} may be recovered by a mapping η₂: U→Vthat maps to output representation V. As discussed herein, η₂ may beexpressed as a parametric function of some parameter set Γ: {right arrowover (v)}=η₂({right arrow over (u)};Γ). Values for parameter set Γ maybe estimated using machine learning techniques, such as feedforwardneural networks and Gaussian processes. In this example, in contrast tothe example provided above with respect to acts 240 and 250, labelsidentifying the samples in {right arrow over (u)} corresponding to theaxes in V may be required to generate G and η₂.

FIG. 3 depicts an exemplary process 300 for training a set of modelsusing data from multiple chemical sensing units (e.g., chemical sensingunits 100, as shown in FIG. 1C). As described herein at least withrespect to FIGS. 2A and 2B, process 300 is implemented by sequentiallyapplying one or more models to the data from multiple chemical sensingunits. The one or more models may include parameters and/orhyper-parameters stored in a storage device of the chemical sensingsystem. In some embodiments, the parameters are learned using machinelearning techniques, examples of which are described with respect toFIGS. 2A and 2B. A chemical sensing system configured to apply thesequence of one or more models according to the learned parametersand/or hyper-parameters to output signals may, for example, infer achemical composition of an environment from the output signals.

In process 300, the series of models may be expressed as a series offunctions, referred to herein as mappings, that transform input chemicalsensor signals into a series of corresponding representations, alsoreferred to herein as spaces, that may be used to generate an inferenceabout the corresponding semantics (e.g., a concentration of one or moreanalytes) in the environment of the chemical sensing units. FIG. 4 is aflow diagram that illustrates an exemplary series of representationscorresponding to the process of FIG. 3. The flow diagram alsoillustrates a pipeline of information processing, in accordance withsome embodiments, when multiple chemical sensing units are used in thesame application(s) and hence are exposed to the same set/type of odors(across chemical sensing units). In some embodiments, the exampleprocesses illustrated in FIGS. 3 and 4 may omit certain operationsand/or representations, may repeat certain operations, and/or mayintegrate operations and representations associated with any suitableprocess described herein, including, but not limited to, those describedwith respect to FIGS. 2A and 2B.

Returning to FIG. 3, the process 300 begins at operation 310 withaccessing signals from multiple chemical sensing units. Operation 310may correspond to operation 210 of FIG. 2A, with multiple chemicalsensing units producing output signals which are then accessed forfurther processing. FIG. 4 further illustrates an example of operation310, where the chemical sensing units 410, after sensing of analytes415, produce output signals 420. The chemical sensing units 410 may beconfigured as shown in FIG. 1C, and may be configured to communicatewith one another and/or with an external storage device. The signalsaccessed at operation 310 may be accessed from the external storagedevice, received directly from the chemical sensing units 410, oraccessed in any other suitable manner. The signals may be in anysuitable format, examples of which are described herein at least withrespects to FIG. 2A.

For notational convenience, with respect to FIGS. 3 and 4, let xrepresent the signals output from a chemical sensing unit. If M is thenumber of signals produced by the sensor array associated with thatchemical sensing unit, then x=(x₁, x₂, . . . , x_(M)) such that x rangesin an M dimensional space S. As described herein, a chemical sensingunit may produce signals, for example, when exposed to an analyte samplewithin its environment over time, resulting in a time-dependent Mdimensional output. Let A(t) represent the chemical composition (e.g.,concentrations of various analytes) within the environment at time t.According to some embodiments, the chemical composition of theenvironment before the sample was taken (e.g., pre-stimulus) may beconsidered A¹ and the chemical composition of the environment after thesample is taken (e.g., post-stimulus) may be considered as A².

At operation 320, a ζ function may be learned for each chemical sensingunit, mapping signals output from the chemical sensing unit to acorresponding feature representation Z. Operation 320 may correspond tooperation 220 of FIG. 2A, in which signals from a chemical sensing unitare mapped to a feature representation, applied over multiple chemicalsensing units. As shown in FIG. 4, operation 320 may extract features425 from signals 420 to produce feature spaces 430 corresponding to thechemical sensing units 410. A ζ function learned according to operation320 may produce a descriptor z(t), represented as a K dimensional vectorwithin the feature representation Z, based on the signals output from achemical sensing unit at time t. A descriptor z(t) may be considered aunique numeric representation of the output signals in the feature spaceZ. Represented mathematically, a descriptor may be produced by applyingζ over the sensor outputs x for a time window of size Δt, such thatz(t)=ζ(x_([t-Δt,t])). Expanding this expression over the K dimensions ofthe feature space, yields: z(t)=(z₁(t), z₂ (t), . . . . ,z_(K)(t))=(ζ₁(x_([t-Δt,t])), ζ₂(x_([t-Δt,t])), . . . ,ζ_(K)(x_([t-Δt,t])))=ζ(x_([t-Δt,t])). Thus the ζ functions learned atoperation 320 may be considered maps with the range in Z and the domainin the concatenation of space S and the time dimension.

In some embodiments, some signals may not influence the featurerepresentation and thus may be associated with zero weighting in thecalculation of descriptor z(t). Similarly, although a fixed continuousperiod of time may be used for the time window in the expressions above,in some cases discontinued and/or variable periods of time may be used.

As described herein, A(t) may represent the semantics associated withthe signals x(t), where z(t)=ζ(x(t)) is the correspondent descriptor,and where the following characteristics hold:

-   -   (i) By changing the chemical composition of the environment from        A(t₁) to A(t₂) gradually with a continuous process, the        correspondent descriptor in the Z space will change gradually        over a continuous one-dimensional curve from z(t₁) to z(t₂).    -   (ii) If A(t₁) is considered closer to A(t₂) than a chemical        composition A(t₃), then with respect to at least one distance        metric that describes the chemical composition, the        correspondent descriptors, z(t₁) will be closer to z(t₂) than        z(t₃). The Z space in many cases is a metric space.

The above-mentioned characteristics may lead to the formation ofmanifolds in the feature representation Z, which may be referred toherein as Z′. The data distributions (e.g., clusters of data) within Zmay be a transformation of the measured signals into the feature space.The data distributions may be dense where there are more samplesavailable from the correspondent semantics. The dense data distributionsform manifolds, which may be learned for representation of thesemantics. The map ζ is often a homeomorphism.

The set of all possible values of a variable under certain constraintsmay be referred to herein as a manifold. A chemical sensing unitdesigned in accordance with some embodiments may produce values frommeasured signals in a continuous range, resulting in the formation ofcontinuous data distributions and manifolds. The manifolds maycorrespond to various chemical compositions, such that areas that arecloser in the formed manifolds may correspond to more similar chemicalcompositions or smells.

The constraints that limit the measured signals of a chemical sensingunit may be governed by one or more of (i) the characteristics of thechemical composition of the environment, (ii) the chemo-physicalattributes of the binding process between the chemical molecules and thereceptors on the chemical sensing unit, (iii) the chemo-physicalcharacteristics of the receptors and the design of the sensory array ofthe chemical sensing unit, (iv) the design of the chemical sensing unithardware (e.g., the type, the shape and structure of the headspace), (v)the design of the sampling process (e.g., the manner in which samplesare collected and/or exposed to the chemical sensing unit, which may bereferred to herein as a sniffing process), and (vi) the electronicsdesign.

In some embodiments, the areas of the Z space within which implausiblemeasurements exist (e.g., because of the constraints) may be carved out,leading to the formation of subspaces of Z (e.g., the manifolds). Thusthe dynamics of the relations between variables may define the shape ofthe manifolds. Manifold learning is a technique for learning theunderlying dynamics at different points spanning the Z space and thedata distributions. Through manifold learning, the effect of theconstraints on the captured data, and consequently on the distributionsthat form the manifolds, may be implicitly learned.

The measurements from the chemical sensing unit and the ζ function thatmaps the measured signals to the Z space determine the distribution ofdata in the Z space and the shape of the underlying manifolds in the Zspace. In some embodiments, the manifolds are learned by assessing theirsimilarities (e.g., distance in the Z space) through neighborhoodembedding methods. This step can be learned, for example, viaunsupervised manifold learning methods (e.g., Uniform ManifoldApproximation and Projection (UMAP)).

ζ¹, ζ² . . . , ζ^(n) may be defined as functions that map the measuredsignals from the chemical sensing units 1 through n to the correspondingZ space, Z¹, Z², . . . , Z^(n) respectively. Although the chemicalsensing units may have manufacturing differences that lead to variationsbetween signals output from each chemical sensing unit, each may beconfigured to include, within the output signals, information forinterpreting the semantics of their shared environment. This informationmay include, for example, the presence of chemicals (e.g., one or morechemicals for which the sensors of the sensing unit are designed) andtheir concentrations (e.g., chemical composition or odors of interest)with the environment. The corresponding ζ functions may be developed toextract the information content from the output signals via a firstmodel or sub-model for each chemical sensing unit. Therefore, there maybe a one-to-one map between the semantics and the Z spaces for eachsensing unit, which implies existence of an isomorphism (bijectivehomeomorphism) between any pair of Z spaces.

As shown in FIG. 4, the learned ζ maps for extracting the informativedescriptors (e.g., feature vectors) from the measured signals producefeature spaces that include data distributions mapping to the semanticsassociated with the corresponding application. Since the semantics ofthe application may be unique, the information content of datasetsacquired across chemical sensing units should theoretically be similar.When chemical sensors of similar types (e.g., types sensitive to aparticular chemical or family of chemicals) are used across chemicalsensing units, similar information content of the datasets across thechemical sensing units may lead to formation of similar manifolds.

Each Z space may be a metric space and distance in the Z spacerepresents the similarity of the semantics (e.g., chemical compositions)within the application. As shown in FIG. 4, due to the characteristicsof the metric space, clusters form. Each cluster may represent amanifold, a dense data structure where information about commonsemantics may be concentrated. When the semantics are similar acrosssensing units, the formation of clusters in the feature spaces Z mayalso be similar.

As discussed above, multiple instances of a same sensing unit may havevariations in chemo-physical characteristics of the individual sensorsintroduced, for example, during manufacturing. Such differences may endup yielding some variations in the output of the sensors upon exposureto an environment having the same chemical composition. In addition tothe measured signal from two replications of the same sensing unitsbeing different, the (learned) ζ maps for extracting information fromthe measured signals may also be different.

Returning to FIG. 3, at operation 330 a φ function may be learned bymapping each feature representation Z to a corresponding latentrepresentation Φ. Operation 330 may correspond to operation 230 of FIG.2A, in which a feature representation is mapped to a latentrepresentation, applied over multiple feature representations. As shownin FIG. 4, latent representation learning 425 may be applied to thefeature spaces 420 to produce latent spaces 440.

For each chemical sensing unit, the descriptors (e.g., feature vectors)generated in a Z space can be applied to a second model or sub-modelthat relates the feature representation Z to a latent representation Φto generate latent vectors corresponding to the feature vectors. Alatent representation Φ can be an inner product space. The latentrepresentation Φ can be of the same dimension as the manifold Z′. As anon-limiting example, when Z′, which represents the manifolds within Z,is a plane embedded in Z, the latent representation Φ may be atwo-dimensional space (e.g., a latent representation, as depicted inFIG. 4). The second sub-model may implement a mapping φ: Z→Φ. Asdiscussed herein, φ may be expressed as a parametric function of someparameter set Λ: {right arrow over (p)}=φ({right arrow over (z)}; Λ).Values for parameter set Λ may be estimated using representationlearning techniques such as employing a feed forward neural network andrecurrent neural networks. In some embodiments, the mapping φ: Z→Φfulfills the following conditions: φ is a continuous mapping between Z′and Φ, φ is bijective from Z′ to Φ, φ⁻¹ is a continuous mapping betweenΦ and Z′, and φ⁻¹ is bijective from Φ and Z′. The above conditions mayfollow from the homeomorphism between Z′ and Φ. The functions φ¹, φ², .. . , φ^(n) may be defined to map the feature spaces to corresponding Φspaces, Φ¹, Φ², . . . , Φ^(n) respectively.

Although the Z spaces may have distribution differences, each includesinformation for interpreting the application-driven semantics in theenvironment, including, for example, to detect chemicals of interest andtheir concentrations. The information for interpreting theapplication-driven semantics may also be present in the latentrepresentations. Thus, as shown in FIG. 4, clusters may form in thelatent spaces representing this information. These clusters may belearned with unsupervised manifold learning, or any other suitabletechnique, as described herein. Across chemical sensing units, someclusters (e.g., in FIG. 4, the clusters represented by the open squaresand the open stars; the clusters represented by the filled circles andplus symbols; the clusters represented by the open circles and the ×symbols) may be located next to each other in the latent spaces. Whentwo clusters are close together in a latent space, their correspondentsemantics (e.g., chemical compositions) may be similar with respect tothe collected observations.

Returning to FIG. 3, at operation 340 a mapping from the Φ spaces Φ¹,Φ², . . . , Φ^(n) to a mutual latent space Φ^(S) may be learned. Asshown in FIG. 4, mutual latent representation learning 445 may beapplied to latent spaces 440 to produce the mutual latent space 450. Insome embodiments a one-to-one map may exist between each of the Φ spacesΦ¹, Φ², . . . , Φ^(n), which in turn implies existence of an isomorphism(bijective homeomorphism) between any pair of the P spaces. Therefore, a(reference) mutual latent space Φ^(S) may be considered that has anisomorphism to each of Φ¹, Φ², . . . , Φ^(n) spaces.

In some cases, the functions φ¹, Φ², . . . , Φ^(n) may be defined suchthat φ^(i)=φ^(j) for all i, j, thereby mapping the feature spaces totheir correspondent Φ spaces such that Φ^(i)=Φ^(j) for all i, j. Itfollows then that Φ^(i)=Φ^(S) for all i since the correspondent Φ spacesare identical. Therefore, in such cases, φ^(i) directly maps the featurespace to the (reference) mutual latent space Φ^(S).

Additionally or alternatively, a (reference) mutual latent space Φ^(S)that has an isomorphism to each of Φ¹, Φ², . . . , Φ^(n) spaces may beconsidered. To build Φ^(S), a map can be trained that transfers any ofthe Φ¹, Φ², . . . , Φ^(n) spaces to another of them (referred to as thereference latent space), or a new Φ^(S) can be created that has aseparate isomorphism with respect to each of the Φ¹, Φ², . . . , Φ^(n)spaces. The individual maps may transform the corresponding Φ^(i) spacesto temporary representations Φ′^(i), that are often sparse andhomomorphic to Φ^(i). The shared map may optimize the presentation of aglobal map Φ^(S), for example with respect to minimal redundancy (e.g.,same cardinality with Φ^(i)) and maximal relevance for a particularapplication (e.g., encoding information relevant to particularinferences, such as analyte composition or concentrations, which may begenerated based on Φ^(S)).

Returning to FIG. 3, at operation 350 an inference block may be learnedbased on the mutual latent representation. As shown in FIG. 4, theinference block 455 may map from values in the mutual latent space 450to inferences, which may represent the results of an identification,quantification, or predication task regarding the semantics detected bythe chemical sensing units 410. For example, an inference may be aquantification of the concentration of one more analytes within asample. In some embodiments, the inference block may be a feed forwardneural network, a support vector machine, a recurrent neural network, along-short-term-memory neural network, or any other suitable statisticalmodel for generating inferences.

FIG. 5 depicts an exemplary system architecture for a chemical sensingsystem comprising many chemical sensing units. The chemical sensingunits may be configured as shown in FIG. 1C, with multiple chemicalsensing units being in communication with one another and/or an externalstorage medium. It should be appreciated that the system architecture ofFIG. 5 may be implemented with any appropriate hardware and/or software,as described herein. For example, the operations shown in FIG. 5,including storing data, accessing data, and processing data, may beperformed as part of a computer program implemented on one or moreprocessors storing instructions on a non-transitory storage medium. Thesystem architecture of FIG. 5 may additionally or alternatively beimplemented in a distributed computing environment, including, forexample, a cloud computing environment.

At operation 510, data from the chemical sensing units may be stored ina data repository 520 (which may correspond to external storage device190 in FIG. 1C, in some embodiments). The data may include valuesrepresenting signals output by the chemical sensing units (e.g., the“sensing modules” shown in operations 510 and 520). The dataadditionally or alternatively may include metadata representinginformation about the corresponding analytes, their concentrations, theenvironment, and/or the configuration or type of chemical sensing unitsbeing used. In some embodiments, the metadata may be associated withsome or all of the signals output by the chemical sensing units. Themetadata may be used to determine labels corresponding to the valuesrepresenting signals output by the chemical sensing units. A set of thelabels and the values to which they correspond may comprise a trainingdataset, which may be used to train at least one model as describedherein.

At operation 530, the data stored in the data repository may be accessed(e.g., “fetched”) from the data repository. This operation maycorrespond, for example, to operation 310 of process 300 in FIG. 3, andmay be carried out according to any of the techniques described hereinat least with respect to FIG. 3. In some embodiments, operation 530 maybe carried out by one or more processors, which may, for example,include a server external to the chemical sensing units.

At operation 540 the data accessed at operation 530, including thevalues representing the signals from each chemical sensing unit, may beprocessed. More particularly, the processing may comprise extractingfeatures from the data, according to any of the techniques describedherein at least with respect to FIGS. 2A-2B, 3-4, and 6-8. Theprocessing at operation 530 may include training a model that maps thedata to a feature representation. As shown in FIG. 5, the results ofoperation 530 may be maps ζ¹, ζ², . . . , ζ^(n). These maps may berepresented in any suitable manner, including, for example, as valueswithin one or more data structures (e.g., numeric weights within amatrix). Optionally the processed data (e.g., a representation of themaps ζ¹, ζ², . . . , ζ^(n)) may be stored in processed data repository550. Processed data repository 550 may be a shared data repository withraw data repository 520 or may be a separate data repository.

At operation 560, the processed data may be structured for subsequentprocessing, including, for example, a learning process 570. Structuringthe processed data at operation 560 may comprise, for example, combiningthe processed data received from operation 530 with data accessed fromprocessed data repository 550, which may include previously storedprocessed data (e.g., maps ζ¹, ζ², . . . , ζ^(n)). The resultingstructured data may be stored in the processed data repository 550, andmay be accessed, for example, during subsequent instances of operation560.

The structured data, which may be received from operation 560 and/oraccessed from the processed data repository 550, may then be provided asinput to the learning process 570. The learning process 570 may becarried out according to any of the techniques described herein at leastwith respect to FIGS. 3-4 and 6-8, and may include training one or moremodels via machine learning techniques, as described herein. The resultsof the learning process 570 may include trained models that may berepresented in any suitable format, including as values in one or moredata structures (e.g., as weights in a matrix or matrices).

As part of learning process 570, at operation 571, functions φ¹, φ², . .. , φ^(n) may be learned, with the functions mapping data from thefeature representations Z to corresponding latent representations Φ. Theφ¹, φ², . . . , φ^(n) functions may be learned according to any of thetechniques described herein at least with respect to FIGS. 2A-2B, 3-4,and 6-8.

At operation 572, a mutual latent representation may be learnedaccording to any of the techniques described herein at least withrespect to FIGS. 3-4 and 6-8.

At operation 573, an inference block may be learned according to any ofthe techniques described herein at least with respect to FIGS. 3-4, and6-8. Operation 573 may serve to assign context to the mutualrepresentation space, allowing inferences regarding the semantics to bedrawn based on mutual representation values. The inference block of theinformation processing unit may be a feed forward neural network or asupport vector machine (SVM), for example.

In some embodiments, the results of learning system 570, which mayinclude trained models as described herein, may be stored in a modelrepository 580. Model repository 580 may be shared with processed datarepository 550 and/or raw data repository 520 or may be a separate datarepository.

FIGS. 6 and 7 present techniques for leveraging available training datafor a new chemical sensing unit, together with information regardingpreviously-trained models associated with other chemical sensing units,in order to train one or models associated with the new chemical sensingunit. For example, in some embodiments, a limited quantity of trainingdata may be available (e.g., in the form of output signals from the newchemical sensing unit labelled according to the corresponding semantics)and model information from previously-trained models may be leveraged toachieve accurate results despite the limited quantity of training data.In some embodiments, the information regarding previously-trained modelsmay be accessed from a storage medium such as the model repository 580.In some embodiments, the information regarding previously-trained modelsmay be stored by the chemical sensing units themselves, and may beaccessed accordingly.

FIG. 6 depicts an exemplary process for training a set of models usingdata from previously-trained models and data from at least oneadditional chemical sensing unit (e.g., a new chemical sensing unit).The exemplary process of FIG. 6 involves learning a map that transformsthe output signals of the new chemical sensing unit to a mutual latentrepresentation with limited training data. More particularly, as part oflearning a latent representation corresponding to the new chemicalsensing unit, information representing the latent representations of thepreviously-trained models may be leveraged to learn the new latentrepresentation. This may further facilitate the calculation ofparameters mapping the new latent representation to the latentrepresentation to the mutual latent representation.

Unlike supervised learning techniques in which a generalization task maybe learned by training a model using many labeled observations (e.g.,for every chemical sensing unit), semi-supervised learning can beleveraged to learn patterns (e.g., the maps for a new sensing unit) witha reduced quantity of labeled observations. In general, the accuracy ofthe learned maps increases with more observations; however, anacceptable level of accuracy can be achieved by using limitedobservations and leveraging the existence of the maps learned forchemical sensing units that include similar chemical sensors. In someexperiments described in more detail below, an 80% accuracy was achievedfor a new (e.g., previously unseen) chemical sensing unit by trainingthe model(s) associated with an existing chemical sensing system with areduced quantity of data (2% of the dataset used to initially train thesystem) from the new chemical sensing unit.

In FIG. 6, process 600 begins at operation 610, with accessinginformation associated with 1 . . . n chemical sensing units. Thesechemical sensing units may be incorporated as a portion of a chemicalsensing system for which models (e.g. as described herein at least withrespect to FIGS. 3-4) have already been trained.

At operation 620, signals from a new chemical sensing unit n+1 areaccessed. These signals may have corresponding labels, and together thesignals and labels may comprise a data set that can be used as trainingdata for training one or more models associated with the new chemicalsensing unit. The quantity of training data associated with the signalsaccessed from the n+1 chemical sensing unit at operation 620 may be lessthan the quantity of training data used to train the models associatedwith the n chemical sensing units (e.g., less than 10%, such as 5%, or2%).

At operation 630, a ζ function mapping the accessed signals from the newchemical sensing unit n+1 to a feature representation Z^(n+1) may belearned. Operation 630 may be carried out according to the techniquesfor feature extraction described herein at least with respect to FIGS.2A-2B, and 3-4. Operation 630 may alternatively or additionally use theinformation associated with the n chemical sensing units, accessed atoperation 610, to learn the new function.

At operation 640, a latent representation Φ^(n+1) is learned for thechemical sensing unit n+1 associated with the feature space Z^(n+1) fromoperation 630. In some embodiments, a new map φ^(n+1) may be learned,where φ^(n+1): Z^(n+1)→Φ^(n+1), according to any of the techniquesdescribed herein at least with respect to FIGS. 2A-2B and 3-4. In someembodiments, information representing the functions φ¹, φ², . . . ,φ^(n) associated with the chemical sensing units 1 . . . n may be usedas part of learning the φ^(n+1) map. In some embodiments, the map fromZ^(n+1)→Φ^(n+1) may be expressed as combination of the functions Φ¹, φ²,. . . , φ^(n).

At operation 650, a map from the latent representation Φ^(n+1) to amutual latent representation Φ^(s) is learned. In some embodiments,there is a one-to-one map between all Φ spaces. The previously-learnedmaps associated with the chemical sensing units 1 . . . n fromΦ^(1 . . . n) to Φ^(s) may be used to learn the isomorphism map fromΦ^(n+1) to the reference latent space Φ^(s). The map from Φ^(n+1) toΦ^(s) can be learned by combining the previously-learned maps for thechemical sensing units 1 . . . n or as a new map.

In some embodiments, a partially labeled dataset may provide weaksupervision to map individual latent spaces Φ^(i) to the final mutuallatent space Φ^(S), where the following objectives direct theconstruction of a loss function used for the learning process:

-   -   The manifolds should be correspondent and hence the neighborhood        characteristics of the Φ^(i) will be equivalent to the        neighborhood characteristics of Φ^(S). For example, the mapped        representation of close/far samples in Φ^(i) to the Φ^(S) will        stay close/far.    -   The semantics of the latent representations Φ^(i) should match        the semantics in Φ^(S) so that latent variables in Φ^(i) spaces        with same or very similar semantics will match latent variables        in Φ^(S) that are close to each other (respecting the similarity        of their semantics) and latent variables in Φ^(i) spaces with        different or very distinguishable semantics will match latent        variables in Φ^(S) that are far each other (respecting the        dissimilarity of their semantics).

According to some embodiments, there may be instances in which thechemical composition of the environment at a particular point in timedepends on the sequence of chemical compositions during at least oneprevious point in time. In such instances, the transitions from onechemical composition to another may also be learned and represented inthe mutual latent representation to improve information processingcapabilities.

FIG. 7 illustrates a sequential relationship described by transitionsfrom one data distribution to another data distribution. Sequentialrelationships can be captured by sequential models for inferencepurposes. Sequential relationships may also provide information aboutthe transitionary states (e.g., data distributions in a latentrepresentation). Thus the sequential relationships may provide supportand information about the semantics, and may therefore facilitatebuilding isomorphism between the Φ^(i) and Φ^(S).

In FIG. 7, C₁, C₂, C₃, and C′ represent four different datadistributions. The traverse from C1 to C′ represents a semantic that isdistinguishable from the semantic associated with the transition from C1to C2 and then C3. For example, consider a sequential relationship in alatent representation Φ^(i), that involves a traverse through threedistributions; this may correspond to the same sequential relationshipin another latent space Φ^(i) that traverses through threedistributions. The correspondence between sequential relationshipsacross chemical sensing units, supports the likelihood of correspondenceof the involved distributions in the transitions respectively. Hence thesemantics of unlabeled distributions in a latent representation would betied to the semantics of the correspondent distributions in the otherlatent representations considering the sequential relationships.

FIG. 8 further explains a technique for learning sequentialrelationships in accordance with some embodiments. As shown in thefigure, sequential relationships may arise between data distributions inthe latent representations 840: for example, 841 a→841 b→841 c in thelatent space Φ¹; 842 a→842 b→842 c in the latent space Φ²; and 843 a→843b→843 c in the latent space Φ³. When the chemical sensing units 810 areexposed to the same semantics, it follows that the resulting sequentialrelationships should have a correspondence. As shown in FIG. 8, themutual latent space Φ^(S) 850 expresses a corresponding sequentialrelationship 851 a→881 b→851 c. Given latent representations havingcorresponding sequential relationships across chemical sensing units(e.g., where the chemical sensing units include chemical sensors thatwere designed/used for similar applications) the correspondence may beleveraged during the process of building the isomorphism from Φ^(i) toΦ^(S).

Additionally or alternatively, sequential relationships may be leveragedas part of the inference block. The inference block of the informationprocessing unit should be able to model sequential relationships, andrecurrent neural networks and long-short-term-memory based networkscould be used to build such inference blocks, for example.

FIG. 9 depicts an exemplary process 900 for using a trained set ofmodels to generate an inference based on input signals from a chemicalsensing unit. A set of models, trained according to the techniquesdescribed herein at least with respect to FIGS. 3-4 and 6-8, may be usedto generate an inference based on new data acquired from a chemicalsensing unit. The set of models may be trained on data acquired fromchemical sensing unit(s) as described herein, or pre-trained models maybe accessed from a storage medium (e.g., model repository 580).

At operation 910, new data may be accessed in the form of signals from achemical sensing unit m. The new data may be in any suitable format, asdescribed herein. The new data may be associated with the currentsemantics of the corresponding environment.

At operation 920, a feature vector may be generated by applying theappropriate ζ^(m) function (e.g., via a model of the set of models) tothe signals accessed at operation 910. The result may be a descriptor inZ^(m) space, reflecting the features extracted from the signals.

At operation 930, the feature vector may be provided as input to afunction φ^(m) (e.g., via a model of the set of models) that transformsthe values in Z^(m) into values in the latent representation Φ^(m).

At operation 940, the values in the latent space Φ^(m) may be mapped tothe mutual latent representation Φ^(s).

At operation 950, the inference block generates an inference based onthe values in the mutual latent representation. As described herein, theinference may include identification, quantification, and predictionresults

FIG. 10 is an exemplary process for using a trained set of models todetermine a concentration of an analyte in a sample based on inputsignals from a plurality of chemical sensing units. A set of models,trained according to the techniques described herein at least withrespect to FIGS. 3-4 and 6-8, may be used to generate an inference basedon new data acquired from a chemical sensing unit. The set of models maybe trained on data acquired from chemical sensing unit(s) as describedherein, or pre-trained models may be accessed from a storage medium(e.g., model repository 580).

At operation 1010, new data may be accessed in the form of signals froma chemical sensing unit having been exposed to at least one analyte ofinterest within a sample. The new data may be in any suitable format, asdescribed herein.

At operation 1020, a feature vector may be generated by applying a modelof the set of trained models to the signals accessed at operation 1010.The result may be a descriptor (e.g., feature values) reflecting thefeatures extracted from the signals.

At operation 1030, the feature vector may be provided as input to amodel of the set of models that transforms the values in the featurevector into values in the latent representation.

At operation 1040, the values in the latent representation may be mappedto the mutual latent representation,

At step 1050, the inference block generates an inference based on thevalues in the mutual latent representation. In the example of FIG. 10,the inference is a concentration of at least one analyte in the sampleto which the sensors of the chemical sensing unit were exposed.

FIGS. 11A, 11B, and 11C relate to a non-limiting, exemplaryimplementation of some of the techniques as described herein, carriedout over a proprietary data set. In this example, the dataset includesvalues representing signals (e.g., the time-dependent responses) ofeight chemical sensing units for a total of 11,000 chemical samples fromfive analytes: air, oranges, garlic cloves, Smirnoff vodka, andpassionfruit extract. Each time-dependent response may be referred toherein as a cycle, and may include 32 time-series data, corresponding tothe 32 chemical sensors of the chemical sensing units, respectively.

In this example, the chemical sensing units may be situated within adevice known as a ‘sniffer’, which may contain a mechanism for drawinggaseous samples into an area above the sensing elements for a period ofcontrolled exposure. The gaseous sample may be drawn through a nozzle,which may be held near the analyte for delivery to the sensing elements.Each cycle may be composed of: a baseline period, during which thebackground time-dependent response is established; an exposure period,during which the sensing unit is exposed to the analyte andtime-dependent responses are collected; and a recovery period, duringwhich the time-dependent responses recover toward the backgroundtime-dependent response.

In FIGS. 11A through 11C, the analytes air, garlic, orange, passionextract, and Smirnoff vodka are represented by filled circles, opencircles, filled squares, open squares, and filled diamonds,respectively. FIGS. 11A and 11B depict the latent representations Φ^(i)(more particularly, Φ¹ and Φ²) generated by the mappings φ^(i):Z^(i)→Φ^(i) learned for each sensing unit, according to the techniquesdescribed herein. FIG. 11 C depicts a (reference) mutual latent spaceΦ^(S) which, in this example, is isomorphic to each of the Φ¹, Φ², . . ., Φ⁸ latent spaces that correspond respectively to the eight sensingunits.

In the illustrated example, the data set, comprising 11,000 cyclesacross eight devices, is utilized to showcase the output at variousstages of the techniques described herein. The chemical sensing unitsemployed in this example produce time-dependent responses with asampling rate of 1 Hz; over 40 seconds, each sensing element outputs aseries of readings throughout a cycle for a total of 40 such readings.Each reading in the cycle is represented by f₁ which is a 32-elementreading normalized with respect to a baseline vector, β. Morespecifically, each reading α_(i) is divided elementwise by the baselinevector, β, followed by a subtraction of the value 1:

${f_{i} = \begin{bmatrix}f_{1} \\\begin{matrix}f_{2} \\\vdots\end{matrix} \\f_{32}\end{bmatrix}},{\alpha_{i} = \begin{bmatrix}\alpha_{1} \\\begin{matrix}\alpha_{2} \\\vdots\end{matrix} \\\alpha_{32}\end{bmatrix}},{\beta = {{\begin{bmatrix}\beta_{1} \\\begin{matrix}\beta_{2} \\\vdots\end{matrix} \\\beta_{32}\end{bmatrix}\mspace{14mu} {where}\mspace{14mu} f_{i}} = {\frac{\alpha_{i}}{\beta_{i}} - 1}}}$

In this example, the resulting descriptor for a single cycle is a matrixof size (40, 32), and the dataset comprises 11,000 such cycles. Thus theresulting set of descriptors is a matrix of size (11000, 40, 32). Theset of descriptors may be further divided into eight descriptor sets ofsize (n_(i), 40, 32) where n_(i) is the number of samples collected viasensing unit i.

In this example, a mapping φ^(i): Z^(i)→Φ^(i) is learned for eachchemical sensing unit. Two non-limiting embodiments of the mapping tothe mutual latent space are considered in this example. In the firstembodiment, the mapping φ^(i): Z^(i)→Φ^(i) is decoupled from the mappingof each Φ^(i) to Φ^(S) followed by a mapping of all Φ^(i) to Φ^(S), suchthat φ^(i) and φ^(j) for i,j∈{1, 2, . . . n} are not necessarily equal.In the second embodiment, the functions Φ¹, Φ², . . . , Φn can belearned such that φ¹=φ²= . . . =φ^(n), thereby directly mapping eachZ^(i) to Φ^(S).

For this example, in either embodiment, convolutional neural networksmay be deployed to transform data associated with each cycle intok-dimensional descriptors (where k in this example is equal to 256). Thefirst embodiment may use unique convolutional neural networks for eachchemical sensing unit to generate the descriptor (e.g., a featurevector) followed by manifold learning for a reduction of each descriptorto a latent representation (e.g., a three-dimensional vector). Anadditional neural network may then be used to learn the mapping of eachthree-dimensional vector into the mutual latent space.

In the second embodiment, a single convolutional neural network maylearn the mapping directly using the entire data set. The mappingsφ^(i): Z^(i)→Φ^(i) are learned such that φ¹=φ²= . . . =φ^(n) and henceφ^(i) maps Z^(i) to Φ^(S) directly; i.e. the map from Φ^(i) to Φ^(S) isthe identity map for i∈{1, 2, . . . n}.

Vectors with three real-valued elements, such as those within the latentrepresentations and mutual latent representations in this example, canbe associated with points in three-dimensional space. Each vector with256 elements can be associated with a point in 256-dimensional space. Atransformed descriptor set of size (n, 256) can be associated with npoints in 256-dimensional space (e.g., feature space Z). Points in thisspace may be close/further in proximity to one another if thecorresponding semantics are more similar/dissimilar according to a givenmetric. For example, for a particular chemical sensing unit, twodescriptors both corresponding to the semantics of an orange will bemore similar than a descriptor corresponding to the semantics of anorange and a descriptor corresponding to the semantics of garlic.

In the following step of this example, manifold learning may beperformed (e.g., using techniques such as t-SNE or UMAP). Manifoldlearning may be used to learn the underlying structure of the dataspace, thereby reducing the dimensionality of the data from 256 to 3,for example. It may be desirable that this method be non-parametric, andthat it preserve the locality of nearby semantics in the original spaceafter reducing the dimension. This may preserve embedded informationregarding the chemical characteristics of the original datadistributions. If two points in the original 256-dimensional space areclose to one other, then the corresponding points may stay close in thenew space created by reduction of dimensionality. Similarly, if twopoints in the original 256-dimensional space are far from one other,then the corresponding points may stay far from one another in the newspace. In some embodiments, manifold learning is performed on the256-dimensional output vectors, generating three-dimensional vectors inthe correspondent space(s).

In the first embodiment, the learning of the map φ^(i): Z^(i)→Φ^(i) isperformed separately for each chemical sensing unit (e.g., with separateconvolutional neural networks). Manifold learning is then performed onthe resulting 256-dimensional vectors in order to generate thecorresponding three-dimensional vectors in Φ^(i) space. Consequently,the Φ^(i) spaces can be viewed in three dimensions for each chemicalsensing unit.

FIG. 11A depicts a space Φ¹ formed by feeding points associated with afirst chemical sensing unit into the trained convolutional neuralnetwork described in the first embodiment, followed by manifold learningusing t-SNE. As shown in the figure, clusters of points may arisecorresponding to particular semantics in an environment (e.g., aircluster 1101 a, garlic cluster 1101 b, orange cluster 1101 c,passionfruit extract cluster 1101 d, and Smirnoff vodka cluster 1101 e).

FIG. 11B depicts a space Φ² formed by feeding points associated with asecond chemical sensing unit into the trained convolutional neuralnetwork described in the first embodiment, followed by manifold learningusing t-SNE. As shown in the figure, clusters of points may arisecorresponding to particular semantics in an environment (e.g., aircluster 1102 a, garlic cluster 1102 b, orange cluster 1102 c,passionfruit extract cluster 1102 d, and Smirnoff vodka cluster 1102 e).The clusters of FIG. 11B may be different from the clusters of FIG. 11A,but may correspond to the same semantics. For example, the firstchemical sensing unit and second chemical sensing unit may be situatedin the same environment (e.g. the same headspace), and may be exposed tothe same analytes in the same concentrations.

In some cases, for the first embodiment, there may be no similarityconstrains (e.g., no parameter sharing) in the process of building theφ^(i) maps, and thus the maps φ^(i) and the corresponding spaces neednot be equivalent (i.e., Φ¹≠Φ²≠ . . . ≠Φ⁸). In the second embodiment,the φ^(i) maps are learned simultaneously, via the same convolutionalneural network, and thus may be the same.

In the first embodiment, a neural network may then be used to learn themutual representation Φ^(S), using as input the three-dimensionalvectors produced as a result of manifold learning performed on the256-dimensional output vectors produced by the trained convolutionalneural networks associated with each chemical sensing unit. The secondembodiment may use a single convolutional neural network trained on theentire dataset from all chemical sensing units to directly produce256-dimensional vectors on which manifold learning can be performed togenerate three-dimensional vectors in the space Φ^(S). In either case,the final three-dimensional vectors within the mutual latent space Φ^(s)such that points representing similar semantics may appear close to oneanother in space. In other words, the signals from the differentchemical sensing units, which may be different from one another (e.g.,due to variations in the manufacturing process), are mapped to the samespace in the mutual latent representation.

FIG. 11C depicts a space Φ^(S) formed by feeding points associated withall the chemical sensing units of this example into the convolutionalneural network described in the second embodiment, followed by manifoldlearning using t-SNE. In the first embodiment, a similar plot may beproduced by plotting the output of the final neural network which learnsa mapping from each Φ^(i) to the shared representation Φ^(S).

In the following step of this example, subsequent to the learning of themutual representation, an appropriate inference model (e.g.,corresponding to the inference block described elsewhere herein) may bechosen for the purpose of making inferences (e.g. discriminatingbetween) analytes. Such models may include, but are not limited to,additional layers trained to classify samples, additional neuralnetworks, or classical machine learning methods such as support vectormachines. Such models may relate values in the mutual latentrepresentation with a unique semantics that may correspond to a uniquechemical composition (pure or complex chemical compositions).

An illustrative implementation of a computer system 1200 that may beused in connection with any of the embodiments of the technologydescribed herein is shown in FIG. 12. The computer system 1200 includesone or more processors 1210 and one or more articles of manufacture thatcomprise non-transitory computer-readable storage media (e.g., memory1220 and one or more non-volatile storage media 1230). The processor1210 may control writing data to and reading data from the memory 1220and the non-volatile storage device 1230 in any suitable manner, as theaspects of the technology described herein are not limited in thisrespect. To perform any of the functionality described herein, theprocessor 1210 may execute one or more processor-executable instructionsstored in one or more non-transitory computer-readable storage media(e.g., the memory 1220), which may serve as non-transitorycomputer-readable storage media storing processor-executableinstructions for execution by the processor 1210.

Computing device 1200 may also include a network input/output (I/O)interface 1240 via which the computing device may communicate with othercomputing devices (e.g., over a network), and may also include one ormore user I/O interfaces 1250, via which the computing device mayprovide output to and receive input from a user. The user I/O interfacesmay include devices such as a keyboard, a mouse, a microphone, a displaydevice (e.g., a monitor or touch screen), speakers, a camera, and/orvarious other types of I/O devices.

The above-described embodiments can be implemented in any of numerousways. For example, the embodiments may be implemented using hardware,software or a combination thereof. When implemented in software, thesoftware code can be executed on any suitable processor (e.g., amicroprocessor) or collection of processors, whether provided in asingle computing device or distributed among multiple computing devices.It should be appreciated that any component or collection of componentsthat perform the functions described above can be generically consideredas one or more controllers that control the above-discussed functions.The one or more controllers can be implemented in numerous ways, such aswith dedicated hardware, or with general purpose hardware (e.g., one ormore processors) that is programmed using microcode or software toperform the functions recited above.

In this respect, it should be appreciated that one implementation of theembodiments described herein comprises at least one computer-readablestorage medium (e.g., RAM, ROM, EEPROM, flash memory or other memorytechnology, CD-ROM, digital versatile disks (DVD) or other optical diskstorage, magnetic cassettes, magnetic tape, magnetic disk storage orother magnetic storage devices, or other tangible, non-transitorycomputer-readable storage medium) encoded with a computer program (i.e.,a plurality of executable instructions) that, when executed on one ormore processors, performs the above-discussed functions of one or moreembodiments. The computer-readable medium may be transportable such thatthe program stored thereon can be loaded onto any computing device toimplement aspects of the techniques discussed herein. In addition, itshould be appreciated that the reference to a computer program which,when executed, performs any of the above-discussed functions, is notlimited to an application program running on a host computer. Rather,the terms computer program and software are used herein in a genericsense to reference any type of computer code (e.g., applicationsoftware, firmware, microcode, or any other form of computerinstruction) that can be employed to program one or more processors toimplement aspects of the techniques discussed herein.

The foregoing description of implementations provides illustration anddescription, but is not intended to be exhaustive or to limit theimplementations to the precise form disclosed. Modifications andvariations are possible in light of the above teachings or may beacquired from practice of the implementations. In other implementationsthe methods depicted in these figures may include fewer operations,different operations, differently ordered operations, and/or additionaloperations. Further, non-dependent blocks may be performed in parallel.

It will be apparent that example aspects, as described above, may beimplemented in many different forms of software, firmware, and hardwarein the implementations illustrated in the figures. Further, certainportions of the implementations may be implemented as a “module” thatperforms one or more functions. This module may include hardware, suchas a processor, an application-specific integrated circuit (ASIC), or afield-programmable gate array (FPGA), or a combination of hardware andsoftware.

1. A method of training a set of models associated with a first chemicalsensing unit, using information associated with a plurality of chemicalsensing units not including the first chemical sensing unit, the methodcomprising: accessing the information associated with the plurality ofchemical sensing units, wherein the information relates a plurality ofsignals output from the plurality of chemical sensing units to a mutuallatent representation; accessing a training dataset including valuesrepresenting signals output from the first chemical sensing unit; andtraining the set of models associated with the first chemical sensingunit, using the training dataset and the information associated with theplurality of chemical sensing units, wherein training the set of modelscomprises: training a first model of the set of models to relate thevalues representing the signals output from the first chemical sensingunit to a feature representation; training a second model of the set ofmodels to relate the feature representation to a latent representation;and training a third model to relate the latent representation to themutual latent representation.
 2. The method of claim 1, wherein theinformation associated with the plurality of chemical sensing unitscomprises: at least one mapping between a plurality of latentrepresentations associated with the plurality of chemical sensing unitsand the mutual latent representation.
 3. The method of claim 2, whereintraining the third model to relate the latent representation to themutual latent representation comprises: determining a mapping betweenthe latent representation and the mutual latent representation using theat least one mapping between the plurality of latent representations andthe mutual latent representation.
 4. The method of claim 3, wherein thedetermined mapping between the latent representation and the mutuallatent representation comprises a combination of multiple mappings ofthe at least one mapping between the plurality of latent representationsand the mutual latent representation.
 5. The method of claim 2, whereinthe information associated with the plurality of chemical sensing unitscomprises: at least one mapping between a plurality of featurerepresentations associated with the plurality of chemical sensing unitsand the plurality of latent representations associated with theplurality of chemical sensing units.
 6. The method of claim 5, whereintraining the second model to relate the feature representation to thelatent representation comprises: determining a mapping between thefeature representation and the latent representation, using the at leastone mapping between the plurality of feature representations and theplurality of latent representations.
 7. The method of claim 6, whereindetermining the mapping between the feature representation and thelatent representation comprises combining multiple mappings of the atleast one mapping between the plurality of feature representations andthe plurality of latent representations.
 8. The method of claim 1,wherein training the first model comprises using a manifold learningtechnique, a neighborhood embedding technique, an unsupervised learningtechnique, or any combination thereof.
 9. The method of claim 1, whereinthe second model comprises a neural network model.
 10. The method ofclaim 9, wherein the neural network model comprises a feed forwardneural network, a recurrent neural network, a convolutional neuralnetwork, or any combination thereof.
 11. The method of claim 10, whereinthe third model comprises a neural network model.
 12. The method ofclaim 11, wherein the neural network model comprises a feed forwardneural network, a recurrent neural network, a convolutional neuralnetwork, or any combination thereof.
 13. A system comprising: at leastone computer processor; a first chemical sensing unit; a plurality ofchemical sensing units not including the first chemical sensing unit;and at least one non-transitory computer-readable storage medium storingprocessor-executable instructions that, when executed by the at leastone computer processor, cause the at least one computer processor toperform a method of training a set of models associated with the firstchemical sensing unit using information associated with the plurality ofchemical sensing units, the method comprising: accessing the informationassociated with the plurality of chemical sensing units, wherein theinformation relates a plurality of signals output from the plurality ofchemical sensing units to a mutual latent representation; accessing atraining dataset including values representing signals output from thefirst chemical sensing unit; and training the set of models associatedwith the first chemical sensing unit using the training dataset and theinformation associated with the plurality of chemical sensing units,wherein training the set of models comprises: training a first model ofthe set of models to relate the values representing the signals outputfrom the first chemical sensing unit to a feature representation;training a second model of the set of models to relate the featurerepresentation to a latent representation; and training a third model torelate the latent representation to the mutual latent representation.14. The system of claim 13, wherein the information associated with theplurality of chemical sensing units comprises: at least one mappingbetween a plurality of latent representations associated with theplurality of chemical sensing units and the mutual latentrepresentation.
 15. The system of claim 14, wherein training the thirdmodel to relate the latent representation to the mutual latentrepresentation comprises: determining a mapping between the latentrepresentation and the mutual latent representation using the at leastone mapping between the plurality of latent representations and themutual latent representation.
 16. The system of claim 15, wherein thedetermined mapping between the latent representation and the mutuallatent representation comprises a combination of multiple mappings ofthe at least one mapping between the plurality of latent representationsand the mutual latent representation.
 17. A system comprising: at leastone computer processor; and at least one non-transitorycomputer-readable storage medium storing processor-executableinstructions that, when executed by the at least one computer processor,cause the at least one computer processor to: access signals output fromone or more chemical sensing units having a plurality of sensors,wherein the plurality of sensors are configured to sense at least oneanalyte in a sample; and generate an inference regarding the at leastone analyte in the sample by: providing the received signals as input toa first model of a set of models, wherein the first model is trained torelate the signals to a feature representation to generate featurerepresentation values; providing the feature representation values asinput to a second model of the set of models, wherein the second modelis trained to relate the feature representation to a latentrepresentation to generate latent representation values; providing thelatent representation values as input to a third model of the set ofmodels, wherein the third model is trained to relate the latentrepresentation to a mutual latent representation to generate mutuallatent representation values, wherein the mutual latent representationrepresents information from multiple chemical sensing units; andproviding the mutual latent representation values as input to a fourthmodel of the set of models, wherein the fourth model is trained torelate the mutual latent representation to inferences to generate theinference regarding the at least one analyte in the sample.
 18. Thesystem of claim 17, wherein any two or more models of the set of modelsare combined into a single model.
 19. The system of claim 17, whereinthe one or more chemical sensing units comprise a plurality of chemicalsensing units that output differing signals when exposed to a sameanalyte.
 20. The system of claim 17, wherein the signals are stored inthe at least one non-transitory computer-readable storage medium of thesystem.
 21. The system of claim 17, wherein accessing the signals outputfrom the one or more chemical sensing units comprises receiving thesignals directly from the one or more chemical sensing units.
 22. Thesystem of claim 17, wherein the signals are stored in a second storagemedium different from and external to the at least one non-transitorycomputer-readable storage medium.
 23. The system of claim 22, whereinaccessing the signals comprises receiving the signals from the secondstorage medium.
 24. The system of claim 22, wherein the one or morechemical sensing units include the second storage medium.
 25. The systemof claim 17, wherein at least some information representing one or moremodels of the set of models is stored in the at least one non-transitorycomputer-readable storage medium of the system.
 26. The system of claim17, wherein at least some information representing, one or more modelsof the set of models is stored in a second storage medium different fromand external to the at least one non-transitory computer-readablestorage medium.
 27. The system of claim 26, wherein the at least someinformation representing one or more models of the set of models isreceived from the second storage medium.
 28. The system of claim 26,wherein the one or more chemical sensing units include the secondstorage medium.
 29. The system of claim 17, wherein the at least onecomputer processor comprises a plurality of computer processors.
 30. Amethod of generating an inference regarding at least one analyte in asample, the method comprising: accessing signals output from one or morechemical sensing units having a plurality of sensors configured to sensethe at least one analyte in the sample; and generating the inferenceregarding the at least one analyte in the sample by: providing thereceived signals as input to a first model trained to relate the signalsto a feature representation to generate feature representation values;providing the feature representation values as input to a second modeltrained to relate the feature representation to a latent representationto generate latent representation values; providing the latentrepresentation values as input to a third model trained to relate thelatent representation to a mutual latent representation to generatemutual latent representation values, wherein the mutual latentrepresentation represents information from multiple chemical sensingunits; and providing the mutual latent representation values as input toa fourth model trained to relate the mutual latent representation toinferences to generate the inference regarding the at least one analytein the sample.